Current survey of Clifford geometric algebra applications. (English) Zbl 1537.15022
Summary: We extensively survey applications of Clifford Geometric algebra in recent years (mainly 2019–2022). This includes engineering; electric engineering; optical fibers; geographic information systems; geometry; molecular geometry; protein structure; neural networks; artificial intelligence; encryption; physics; signal, image, and video processing; and software.
© 2022 John Wiley & Sons, Ltd.
© 2022 John Wiley & Sons, Ltd.
Keywords:
artificial intelligence; Clifford geometric algebra; engineering; geometry; physics; signal and image processing; softwareReferences:
| [1] | HitzerE. Creative Peace License. https://gaupdate.wordpress.com/2011/12/14/the‐creative‐peace‐license‐14‐dec‐2011/; 2022. |
| [2] | GunterJ. China committed genocide against Uyghurs, independent tribunal rules. BBC News, 09 Dec. 2021, https://www.bbc.com/news/world‐asia‐china‐59595952, accessed 21 Jan; 2022. |
| [3] | HitzerE, NittaT, KuroeY. Applications of Clifford’s geometric algebra. AACA. 2013;23:377‐404. doi:10.1007/s00006‐013‐0378‐4 · Zbl 1269.15022 |
| [4] | BreuilsS, TachibanaK, HitzerE. New applications of Clifford’s geometric algebra. AACA. 2022;32(2):17. doi:10.1007/s00006‐021‐01196‐7 · Zbl 1490.15036 |
| [5] | CliffordWK. Applications of Grassmann’s extensive algebra. Am J Math. 1878;1(4):350‐358. URL: https://www.jstor.org/stable/2369379 · JFM 10.0297.02 |
| [6] | GrassmannHG, KannenbergLC. Extension Theory (Die Ausdehnungslehre von 1862), Vol. 19: History of Mathematics, Sources, American Mathematical Society, Rhode Island, London Mathematical Society; 2000. · Zbl 0953.01025 |
| [7] | HamiltonWR. Elements of Quaternions. 3rd ed.London: Chelsea Pub Co; 2022. URL: https://archive.org/details/elementsquaterni00hamirich/page/n5/mode/2up |
| [8] | HestenesD, LiH, RockwoodA. New algebraic tools for classical geometry. Geometric Computing with Clifford Algebras. Berlin: Springer; 2001. · Zbl 1073.68847 |
| [9] | DorstL, FontijneD, MannS. Geometric Algebra for Computer Science: An Object‐Oriented Approach to Geometry. Burlington (MA), Morgan Kaufmann Series: Elsevier; 2007. |
| [10] | HitzerE, TachibanaK, BuchholzS, YuI. Carrier method for the general evaluation and control of pose, molecular conformation, tracking, and the like. Adv App Cliff Alg. 2009;19(2):339‐364. doi:10.1007/s00006‐009‐0160‐9 Preprint: https://www.researchgate.net/publication/226288320_Carrier_Method_for_the_General_Evaluation_and_Control_of_Pose_Molecular_Conformation_Tracking_and_the_Like · Zbl 1187.15026 |
| [11] | HestenesD, SobczykG. Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics. Dordrecht: Kluwer; 1992. |
| [12] | LounestoP. Clifford Algebras and Spinors. Cambridge (UK): Cambridge University Press; 2001. · Zbl 0973.15022 |
| [13] | BourbakiN. Elements of mathematics, lie groups and lie algebras, Chapters 7-9. translated by Pressley, A. Berlin: Springer; 2005. Chapter 9, paragraph 9, number 1. · Zbl 1139.17002 |
| [14] | ChevalleyC. The algebraic theory of spinors. 1954. · Zbl 0057.25901 |
| [15] | HelmstetterJ, MicaliA. Quadratic Mappings and Clifford Algebras. 2008. · Zbl 1144.15025 |
| [16] | LamTY. The algebraic theory of quadratic forms. New York: W.A. Benjamin, Inc; 1973. Chapter 5. |
| [17] | PorteousIR. Clifford Algebras and the Classical Groups. Cambridge (UK): Cambridge University Press; 1995. · Zbl 0855.15019 |
| [18] | FalcaoMI, MalonekHR. Generalized Exponentials through Appell sets in [( {\mathbb{R}}^{n+1} \]\) and Bessel functions. AIP Conf Proc. 2007;936:738‐741. doi:10.1063/1.2790257 · Zbl 1152.33306 |
| [19] | BreuilsS, TachibanaK, HitzerE. Introduction to Clifford’s Geometric Algebra. preprint, 10 pp. https://vixra.org/abs/2108.0145; 2021. |
| [20] | HitzerE. Introduction to Clifford’s geometric algebra. SICE J Control Meas Syst Integr. 2012;51(4):338‐350. Preprint: https://arxiv.org/abs/1306.1660 |
| [21] | AnglèsP. Conformal groups in geometry and Spin structures. Birkhäuser Boston; 2008. · Zbl 1136.53001 |
| [22] | Blaine LawsonH, MichelsohnM.‐L. Spin Geometry. 1990. |
| [23] | CrumeyrolleA. Algèbres de Clifford et spineurs, Vol. 3: Université de Toulouse; 1974. |
| [24] | CrumeyrolleA. Fibrations spinorielles et twisteurs généralisés. Periodica Math Hungarica. 1975;6‐2:143‐171. · Zbl 0307.53022 |
| [25] | CrumeyrolleA. Spin Fibrations over manifolds and generalized twistors. Proc Symp Pure Math. 1975;27:53‐67. · Zbl 0308.53037 |
| [26] | DeheuvelsR. Formes quadratiques et groupes classiques. 1980. |
| [27] | DeheuvelsR. Tenseurs et spineurs. 1993. · Zbl 0774.53001 |
| [28] | DeligneP. Notes on Spinors. In: P.Deligne (ed.), P.Etingof (ed.), D.S.Freed (ed.), L.C.Jeffrey (ed.), D.Kazhdan (ed.), J.W.Morgan (ed.), D.R.Morrison (ed.), E.Witten (ed.), eds. Quantum Fields and Strings, A course for mathematicians: American Mathematical Society, Providence Rhode Island; 1999. · Zbl 0984.00503 |
| [29] | KaroubiM. Algèbres de Clifford et K‐théorie. Ann Scientifiques de l’E.N.S quatrième série, tome 1. 1964;1:14‐270. |
| [30] | KaroubiM. K‐theory, an introduction. Berlin: Springer‐Verlag; 1978. · Zbl 0382.55002 |
| [31] | MichelsonM‐L. Clifford and spinor cohomology. Am J Math. 1980;106(6):1083‐1146. doi:10.2307/2374181 · Zbl 0462.53035 |
| [32] | AnglèsP, ParrochiaD, MicaliA. L’unification des Mathématiques. 2012. · Zbl 1270.00014 |
| [33] | Bayro‐CorrochanoE. A survey on quaternion algebra and geometric algebra applications in engineering and computer science 1995‐2020. IEEE Access. 2021;9:104,326‐104,355. doi:10.1109/ACCESS.2021.3097756 |
| [34] | Bayro-CorrochanoE. Geometric Algebra Applications Vol. I: Computer Vision, Graphics and Neurocomputing. 2019. · Zbl 1475.68004 |
| [35] | Xambó‐DescampsS. Systems, Patterns and Data Engineering with Geometric Calculi, SEMA SIMAI Springer Series, vol. 13. Cham: Springer Nature Switzerland AG; 2021. |
| [36] | MontoyaFG, BanosR, AlcaydeA, Arrabal‐CamposFM. Geometric algebra for teaching AC circuit theory. Int J Circ Theor Appl. 2021;49(11):3473‐3487. doi:10.1002/cta.3132 |
| [37] | MontoyaFG, EidAH. Formulating the geometric foundation of Clarke, Park, and FBD transformations by means of Clifford’s geometric algebra. Math Meth Appl Sci. 2021:1‐26. doi:10.1002/mma.8038 |
| [38] | MontoyaFG, BanosR, AlcaydeA, Arrabal‐CamposFM. A new approach to single‐phase systems under sinusoidal and non‐sinusoidal supply using geometric algebra. Electr Power Syst Res. 2020;189:106605. doi:10.1016/j.epsr.2020.106605 |
| [39] | MontoyaFG, De LeonF, Arrabal‐CamposFM, AlcaydeA. Determination of instantaneous powers from a novel time‐domain parameter identification method of non‐linear single‐phase circuits. In: IEEE Transactions on Power Delivery; 2021:11. doi:10.1109/TPWRD.2021.3133069 |
| [40] | MontoyaFG, BanosR, AlcaydeA, Arrabal‐CamposFM, Roldan‐PerezJ. Vector geometric algebra in power systems: an updated formulation of apparent power under non‐sinusoidal conditions. Mathematics. 2021;9(11):1295. doi:10.3390/math9111295 |
| [41] | MontoyaFG, BanosR, AlcaydeA, Arrabal‐CamposFM. Analysis of power flow under non‐sinusoidal conditions in the presence of harmonics and interharmonics using geometric algebra. Int J Electr Power Energy Syst. 2019;111:486‐492. doi:10.1016/j.ijepes.2019.04.032 |
| [42] | MontoyaFG, BanosR, AlcaydeA, Arrabal‐CamposFM, VicianaE. Analysis of non‐active power in non‐sinusoidal circuits using geometric algebra. Int J Electr Power Energy Syst. 2020;116:105541. doi:10.1016/j.ijepes.2019.105541 |
| [43] | MontoyaFG, BanosR, AlcaydeA, Arrabal‐CamposFM, Roldan PerezJ. Geometric algebra framework applied to symmetrical balanced three‐phase systems for sinusoidal and non‐sinusoidal voltage supply. Mathematics. 2021;9(11):1259. doi:10.3390/math9111259 |
| [44] | Castro‐NunezM, Londono‐MonsalveD, Castro‐PucheR. Theorems of compensation and Tellegen in non‐sinusoidal circuits via geometric algebra. The J Eng. 2019:3409‐3417. doi:10.1049/joe.2019.0048 |
| [45] | MontoyaFG. Geometric algebra in nonsinusoidal power systems: a case of study for passive compensation. Symmetry. 2019;11(10):1287. doi:10.3390/sym11101287 |
| [46] | MontoyaFG, AlcaydeA, Arrabal‐CamposFM, BanosR. Quadrature current compensation in non‐sinusoidal circuits using geometric algebra and evolutionary algorithms. Energies. 2019;12(4):692. doi:10.3390/en12040692 |
| [47] | CastillaMV, MartinF. A powerful tool for optimal control of energy systems in sustainable buildings: distortion power bivector. Energies. 2021;14(8):2177. doi:10.3390/en14082177 |
| [48] | ÖzdemirZ, EkmekciFN. Electromagnetic curves and Rytov curves based on the hyperbolic split quaternion algebra. Optik. 2022;251:168359. doi:10.1016/j.ijleo.2021.168359 |
| [49] | ÖzdemirZ. A new calculus for the treatment of Rytov’s law in the optical fiber. Optik. 2020;216:164892. doi:10.1016/j.ijleo.2020.164892 |
| [50] | ÖzdemirZ, CansuG, YayliY. Kinematic modeling of Rytov’s law and electromagnetic curves in the optical fiber based on elliptical quaternion algebra. Optik. 2021;230:166334. doi:10.1016/j.ijleo.2021.166334 |
| [51] | Bayro-CorrochanoE. Geometric Algebra Applications Vol. II: Robot Modeling and Control. Heidelberg: Springer Verlag; 2020. · Zbl 1471.93001 |
| [52] | ThiruvengadamS, MillerK. A geometric algebra based higher dimensional approximation method for statics and kinematics of robotic manipulators. AACA. 2020;30:17. doi:10.1007/s00006‐019‐1039‐z; Thiruvengadam S., Miller K., Correction to: A Geometric Algebra Based Higher Dimensional Approximation Method for Statics and Kinematics of Robotic Manipulators. AACA 30:54 (2020). doi:10.1007/s00006‐020‐01079‐3 · Zbl 1448.70008 |
| [53] | ChengS, JiP. Geometric algebra approach to analyzing the singularity of six‐DOF parallel mechanism. J Adv Mech Des Syst Manuf. 2019;13(4). doi:10.1299/jamdsm.2019jamdsm0076 |
| [54] | HuangX, MaC, SuH. A geometric algebra algorithm for the closed‐form forward displacement analysis of 3‐PPS parallel mechanisms. Mech Mach Theory. 2019;137:280‐296. doi:10.1016/j.mechmachtheory.2019.01.035 |
| [55] | LiQ, XuL, ChenQ, ChaiX. Analytical elastostatic stiffness modeling of overconstrained parallel manipulators using geometric algebra and strain energy. ASME J Mech Robot. 2019;11(3):031007. doi:10.1115/1.4043046 |
| [56] | ThiruvengadamS, TanJS, MillerK. A generalized quaternion and Clifford algebra based mathematical methodology to effect multi‐stage rassembling transformations in parallel robots. AACA. 2021;31:39. doi:10.1007 · Zbl 1475.70004 |
| [57] | ZhuG, WeiS, ZhangY, LiaoQ. CGA‐based novel modeling method for solving the forward displacement analysis of 3‐RPR planar parallel mechanism. Mech Mach Theory. 2022;168:104595. doi:10.1016/j.mechmachtheory.2021.104595 |
| [58] | ZhuG, WeiS, ZhangY, LiaoQ. A novel geometric modeling and calculation method for forward displacement analysis of 6‐3 Stewart platforms. Math. 2021;9(4):442. doi:10.3390/math9040442 |
| [59] | HadfieldH, WeiL, LasenbyJ. The forward and inverse kinematics of a delta robot. Advances in Computer Graphics. CGI 2020. Lecture Notes in Computer Science, Vol. 12221. Cham: Springer; 2020. doi:10.1007/978‐3‐030‐61864‐3_38 |
| [60] | HildenbrandD, HrdinaJ, NavratA, et al. Local controllability of snake robots based on CRA, theory and practice. AACA. 2020;30:2. doi:10.1007/s00006‐019‐1022‐8 · Zbl 1457.70005 |
| [61] | HadfieldH, LasenbyJ. Constrained dynamics in conformal and projective geometric algebra. Advances in Computer Graphics. CGI 2020. Lecture Notes in Computer Science. Cham: Springer; 2020:12221. doi:10.1007/978‐3‐030‐61864‐3_39 |
| [62] | MullineuxG, CrippsRJ, CrossB. Fitting a planar quadratic slerp motion. Computer Aided Geom Des. 2020;81:101911. doi:10.1016/j.cagd.2020.101911 · Zbl 1505.65134 |
| [63] | Arellano‐MuroCA, Osuna‐GonzalezG, Castillo‐ToledoB, et al. Newton‐Euler modeling and control of a multi‐copter using motor algebra [( {G}_{3,0,1}^+ \]\). AACA; 30:2020. doi:10.1007/s00006‐020‐1045‐1 |
| [64] | Bayro‐Corrochano E, Garza‐Burgos A.M, Del‐Valle‐Padilla J.L, Geometric intuitive techniques for human machine interaction in medical robotics. Int J of Soc Robotics. 2020;12:91‐112. doi:10.1007/s12369‐019‐00545‐8 |
| [65] | AdornoBV, Marques MarinhoM. DQ Robotics: a library for robot modeling and control. In: IEEE Robotics & Automation Magazine, Vol. 28; 2021:102‐116. doi:10.1109/MRA.2020.2997920 |
| [66] | HuangX, GaoL. Reconstructing three‐dimensional human poses: a combined approach of iterative calculation on skeleton model and conformal geometric algebra. Symmetry. 2019;11(3):301. doi:10.3390/sym11030301 |
| [67] | XuC, WangD, HuangD, et al. Self‐location of unmanned aerial vehicle using conformal geometric algebra. AACA. 2019;29:73. doi:10.1007/s00006‐019‐0992‐x · Zbl 1422.94009 |
| [68] | LiJ, ZhuangY, PengQ, ZhaoL. Band contour‐extraction method based on conformal geometrical algebra for space tumbling targets. Appl Opt. 2021;60:8069‐8081. doi:10.1364/ao.430861 |
| [69] | LiJ, ZhuangY, PengQ, ZhaoL. Pose estimation of non‐cooperative space targets based on cross‐source point cloud fusion. Remote Sens. 2021;13(21):4239. doi:10.3390/rs13214239 |
| [70] | FerrettiE. On the relationship between primal/dual cell complexes of the cell method and primal/dual vector spaces: an application to the cantilever elastic beam with elastic inclusion. Curved Layered Struct. 2019;6(1):77‐89. doi:10.1515/cls‐2019‐0007 |
| [71] | ThiruvengadamS, MurphyM, MillerK. A generalized methodology using conformal geometric algebra for mathematical chemistry. J Math Chem. 2020;58:1737‐1783. doi:10.1007/s10910‐020‐01155‐w · Zbl 1448.92395 |
| [72] | GunnCG, De KeninckS. Geometric algebra and computer graphics, SIGGRAPH ’19. In: ACM SIGGRAPH 2019 Courses, Article No. 12; 2019:1‐140. doi:10.1145/3305366.3328099 |
| [73] | De KeninckS. Non‐parametric realtime rendering of subspace objects in arbitrary geometric algebras. In: GavrilovaM (ed.), ChangJ (ed.), ThalmannN (ed.), HitzerE (ed.), IshikawaH (ed.), eds. Advances in Computer Graphics. CGI 2019. Lecture Notes in Computer Science, Vol. 11542. Cham: Springer; 2019. doi:10.1007/978‐3‐030‐22514‐8_54 |
| [74] | HadfieldH, AchawalS, LasenbyJ, et al. Exploring novel surface representations via an experimental Ray‐Tracer in CGA. AACA. 2021;31:16. doi:10.1007/s00006‐021‐01117‐8 · Zbl 1509.65017 |
| [75] | EidAH, SolimanHY, AbueleninSM. Efficient ray‐tracing procedure for radio wave propagation modeling using homogeneous geometric algebra. Electromagnetics. 2020;40(6):388‐408. doi:10.1080/02726343.2020.1811937 |
| [76] | KamarianakisM, PapagiannakisG. An all‐in‐one geometric algorithm for cutting, tearing, and drilling deformable models. AACA. 2021;31:58. doi:10.1007/s00006‐021‐01151‐6 · Zbl 1481.68045 |
| [77] | WuJ, LopezM, LiuM, ZhuY. Linear geometric algebra rotor estimator for efficient mesh deformation. IET Cyber‐Syst Robot; 2:2020. doi:10.1049/iet‐csr.2020.0010 |
| [78] | Soto‐FrancesVM, Sarabia‐EscrivaEJ, Pinazo‐OjerJM. Consistently oriented dart‐based 3D modelling by means of geometric algebra and combinatorial maps. AACA. 2019;29:19. doi:10.1007/s00006‐018‐0927‐y · Zbl 1452.68248 |
| [79] | Vera SaraviaED. Sobre grupos clasicos de la fisica matematica. Selecciones Mat. 2020;7(02):314‐322. doi:10.17268/sel.mat.2020.02.13 |
| [80] | DechantP‐P. Clifford spinors and root system induction: [( {H}_4 \]\) and the grand antiprism. AACA. 2021;31:57. doi:10.1007/s00006‐021‐01139‐2 · Zbl 1471.15019 |
| [81] | VazJ, MannS. On the Clifford algebraic description of transformations in a 3D Euclidean space. AACA. 2020;30:53. doi:10.1007/s00006‐020‐01080‐w · Zbl 1450.15023 |
| [82] | RennemoJ. The homological projective dual of [( {Sym}^2\mathbb{P}(V) \]\). Compos Math. 2020;156(3):476‐525. doi:10.1112/S0010437X19007772 · Zbl 1453.14053 |
| [83] | MandolesiALG. Blade products and angles between subspaces. AACA. 2021;31:69. doi:10.1007/s00006‐021‐01169‐w · Zbl 1477.15022 |
| [84] | MandolesiALG. Projection factors and generalized real and complex pythagorean theorems. AACA. 2020;30:43. doi:10.1007/s00006‐020‐01070‐y · Zbl 1453.15010 |
| [85] | BizzarriM, LavickaM, VrsekJ. Linear computational approach to interpolations with polynomial Minkowski Pythagorean hodograph curves. J Comput Appl Math. 2019;361:283‐294. doi:10.1016/j.cam.2019.04.029 · Zbl 1416.65048 |
| [86] | HadfieldH, LasenbyJ. Direct linear interpolation of geometric objects in conformal geometric algebra. AACA. 2019;29:85. doi:10.1007/s00006‐019‐1003‐y · Zbl 07111360 |
| [87] | LasenbyJ, HadfieldH, LasenbyAN. Calculating the rotor between conformal objects. AACA. 2019;29:102. doi:10.1007/s00006‐019‐1014‐8 · Zbl 1430.53041 |
| [88] | ShirokovDS. On computing the determinant, other characteristic polynomial coefficients, and inverse in Clifford algebras of arbitrary dimension. Comp Appl Math. 2021;40:173. doi:10.1007/s40314‐021‐01536‐0 · Zbl 1476.65061 |
| [89] | DargysA, AcusA. Exponentials of general multivector in 3D Clifford algebras. Nonlinear Anal Model Control. 2022;27(1):179‐197. doi:10.15388/namc.2022.27.24476 · Zbl 1483.15016 |
| [90] | DorstL. Conformal Villarceau Rotors. AACA. 2019;29:44. doi:10.1007/s00006‐019‐0960‐5 · Zbl 1417.51020 |
| [91] | DorstL. Optimal combination of orientation measurements under angle, axis and chord metrics. Systems, Patterns and Data Engineering with Geometric Calculi, SEMA SIMAI Springer Series, vol. 13. Cham: Springer; 2021. doi:10.1007/978‐3‐030‐74486‐1_4 |
| [92] | De KeninckS, DorstL. Geometric algebra Levenberg‐Marquardt. Advances in Computer Graphics. CGI 2019, Lecture Notes in Computer Science, vol. 11542: Springer; 2019. doi:10.1007/978‐3‐030‐22514‐8_51 |
| [93] | RoelfsM, DudalD, HuybrechsD. Quaternionic step derivative: machine precision differentiation of holomorphic functions using complex quaternions. J Comput Appl Math. 2021;398:113699. doi:10.1016/j.cam.2021.113699 · Zbl 1472.65035 |
| [94] | AlvesR, LavorC, SouzaC, SouzaM. Clifford algebra and discretizable distance geometry. Math Methods Appl Sci. 2018;41:3999‐4346. doi:10.1002/mma.4422 |
| [95] | DorstL. Boolean combination of circular arcs using orthogonal spheres. AACA. 2019;29:41. doi:10.1007/s00006‐019‐0959‐y · Zbl 1417.51014 |
| [96] | CamargoVS, CastelaniEV, FernandesLAF, et al. Geometric algebra to describe the exact discretizable molecular distance geometry problem for an arbitrary dimension. AACA. 2019;29:75. doi:10.1007/s00006‐019‐0995‐7 · Zbl 1430.68361 |
| [97] | LavorC, AlvesR, SouzaM, Aragon JL. NMR protein structure calculation and sphere intersections. Comput Math Biophys. 2020;8(1):89‐101. doi:10.1515/cmb‐2020‐0103 · Zbl 1472.92167 |
| [98] | LavorC, AlvesR. Oriented conformal geometric algebra and the molecular distance geometry problem. AACA. 2019;29:9. doi:10.1007/s00006‐018‐0925‐0 · Zbl 1410.92086 |
| [99] | LavorC, AlvesR. Recent advances on oriented conformal geometric algebra applied to molecular distance geometry. Systems, Patterns and Data Engineering with Geometric Calculi, SEMA SIMAI Springer Series, vol. 13. Cham, Switzerland: Springer; 2021. doi:10.1007/978‐3‐030‐74486‐1_2 |
| [100] | LavorC, AlvesR, FernandesLAF. Linear and geometric algebra approaches for sphere and spherical shell intersections in [( {\mathbb{R}}^n \]\). Expert Syst Appl. 2022;187:115993. doi:10.1016/j.eswa.2021.115993 |
| [101] | ZhangJ, PengX, ChenM. Self‐evident automated proving based on point geometry from the perspective of Wu’s method identity. J Syst Sci Complex. 2019;32:78‐94. doi:10.1007/s11424‐019‐8350‐6 · Zbl 1468.68310 |
| [102] | LiH. Automated theorem proving practice with null geometric algebra. J Syst Sci Complex 32. 2019;32:95‐123. doi:10.1007/s11424‐019‐8354‐2 · Zbl 1468.68297 |
| [103] | LiY, WangZ, ZhaoT. Geometric algebra of singular ruled surfaces. AACA; 31:2021. doi:10.1007/s00006‐020‐01097‐1 · Zbl 1462.53002 |
| [104] | HrdinaJ, NavratA, VasíkP. Geometric algebra for conics. AACA. 2018;28:66. doi:10.1007/s00006‐018‐0879‐2 · Zbl 1398.51045 |
| [105] | HrdinaJ, NavratA, VasikP. Conic fitting in geometric algebra setting. AACA. 2019;29:72. doi:10.1007/s00006‐019‐0989‐5 · Zbl 1428.51015 |
| [106] | LouckaP, VasikP. Algorithms for multi‐conditioned conic fitting in geometric algebra for conics. Advances in Computer Graphics. CGI 2021, Lecture Notes in Computer Science, vol. 13002. Cham: Springer; 2021. doi:10.1007/978‐3‐030‐89029‐2_48 |
| [107] | ByrtusR, DereviankoA, VasikP, et al. On Specific Conic Intersections in GAC and Symbolic Calculations in GAALOPWeb. AACA. 2022;32(2). doi:10.1007/s00006‐021‐01182‐z · Zbl 1478.15033 |
| [108] | EasterRB, HitzerE. Conic and cyclidic sections in double conformal geometric algebra [( {\mathcal{G}}_{8,2} \]\) with computing and visualization using Gaalop. Math Meth Appl Sci. 2020;43:334‐357. doi:10.1002/mma.5887 · Zbl 1476.68285 |
| [109] | BreuilsS, FuchsL, HitzerE, et al. Three‐dimensional quadrics in extended conformal geometric algebras of higher dimensions from control points, implicit equations and axis alignment. AACA. 2019;29:57. doi:10.1007/s00006‐019‐0974‐z · Zbl 1453.51010 |
| [110] | BreuilsS, NozickV, FuchsL, SugimotoA. Efficient representation and manipulation of quadratic surfaces using Geometric Algebras. arXiv preprint arXiv:1903.02444. |
| [111] | HitzerE, SangwineSJ. Foundations of conic conformal geometric algebra and compact versors for rotation, translation and scaling. AACA. 2019;29:96. doi:10.1007/s00006‐019‐1016‐6 · Zbl 1430.51033 |
| [112] | HitzerE. Three‐dimensional quadrics in conformal geometric algebras and their versor transformations. AACA. 2019;29:46. doi:10.1007/s00006‐019‐0964‐1 · Zbl 1416.15019 |
| [113] | ItabaA, MatsunoM. AS‐regularity of geometric algebras of plane cubic curves. J Aust Math Soc. 2021;112(2):1‐25. doi:10.1017/S1446788721000070 |
| [114] | CrippsRJ, CrossB, MullineuxG. Self‐reverse elements and lines in an algebra for 3D Space. AACA. 2020;30(50). doi:10.1007/s00006‐020‐01075‐7 · Zbl 1448.15004 |
| [115] | LavorC, SouzaM, AragonJL. Orthogonality of isometries in the conformal model of the 3D space. Graph Model. 2021;114:101,100‐101,106. doi:10.1016/j.gmod.2021.101100 |
| [116] | ShirokovDS. On inner automorphisms preserving fixed subspaces of Clifford algebras. AACA. 2021;31:30. doi:10.1007/s00006‐021‐01135‐6 · Zbl 1466.15025 |
| [117] | YouzhengZ, YanpingM. Invariants of space line element structure based on projective geometric algebra. IEEE Access. 2020;8:62,610‐62,618. doi:10.1109/ACCESS.2020.2981622 |
| [118] | RoelfsM, DeKeninckS. Graded Symmetry Groups Plane and Simple. Preprint: https://www.researchgate.net/publication/353116859_Graded_Symmetry_Groups_Plane_and_Simple; 2022. |
| [119] | HrdinaJ, NavratA, VasikP, et al. Projective geometric algebra as a subalgebra of conformal geometric algebra. AACA. 2021;31:18. doi:10.1007/s00006‐021‐01118‐7 · Zbl 1462.15028 |
| [120] | DorstL. A Guided Tour to the Plane‐Based Geometric Algebra PGA. version 1.16 Available at https://www.geometricalgebra.net, and https://bivector.net/PGA4CS.html; 2020. |
| [121] | LiH. Geometric interpretations of graded null monomials in conformal geometric algebra. Sci Sin Math. 2021;51(1):179. doi:10.1360/SSM‐2019‐0329 · Zbl 1499.51002 |
| [122] | SobczykG. Notes on Plücker’s relations in geometric algebra. Adv Math. 2020;363:106959. doi:10.1016/j.aim.2019.106959 · Zbl 1470.15021 |
| [123] | BoumaTA, MemowichG. Invertible homogeneous versors are blades. https://www.science.uva.nl/ga/publications; 2001. |
| [124] | VazJ, Roldao da RochaR. An Introduction to Clifford Algebras and Spinors. 2019. · Zbl 1407.15001 |
| [125] | SobczykG. Spheroidal domains and geometric analysis in Euclidean space. Contemp Math [Internet]. 2021;2(3):189‐209. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/875, doi:10.37256/cm.232021875 |
| [126] | VancliffM. Generalizing classical Clifford algebras, graded Clifford algebras and their associated geometry. AACA. 2021;31:43. doi:10.1007/s00006‐021‐01149‐0 · Zbl 1472.15032 |
| [127] | BurlakovIM, BurlakovMP. Geometric structures over hypercomplex algebras. J Math Sci. 2020;245:538‐552. doi:10.1007/s10958‐020‐04710‐7 · Zbl 1442.11072 |
| [128] | AlkheziY. On the geometric algebra and homotopy. J Math Res Arch. 2021;13(2). doi:10.5539/jmr.v13n2p52 |
| [129] | KruglikovB, WintherH. Submaximally symmetric quaternion Hermitian structures. Int J Math. 2020;31(11):2050084. doi:10.1142/S0129167X20500846 · Zbl 1455.53074 |
| [130] | NguyenNHV, PhamM, DoP, PhamC, TachibanaK. Human action recognition method based on conformal geometric algebra and recurrent neural network. Inf Control Syst. 2020;5:2‐11. doi:10.31799/1684‐8853‐2020‐5‐2‐11 |
| [131] | ThiruvengadamS, TanJS, MillerK. Artificial intelligence using hyper‐algebraic networks. Neurocomputing. 2020;399:414‐448. doi:10.1016/j.neucom.2019.12.116 |
| [132] | ThiruvengadamS, TanJS, MillerK. Time series, hidden variables and spatio‐temporal ordinality networks. AACA. 2020;30:37. doi:10.1007/s00006‐020‐01061‐z · Zbl 1444.37064 |
| [133] | LiY, TangH, XieW, LuomW. Multidimensional local binary pattern for hyperspectral image classification. IEEE Trans Geosci Remote Sens. 2022;60:5505113:1‐13. doi:10.1109/TGRS.2021.3069505 |
| [134] | LiY, XiaR, LiuX. Learning shape and motion representations for view invariant skeleton‐based action recognition. Pattern Recognit. 2020;103:107293. doi:10.1016/j.patcog.2020.107293 |
| [135] | LiuX, LiY, XiaR. Rotation‐based spatial‐temporal feature learning from skeleton sequences for action recognition. SIViP 14. 2020:1227‐1234. doi:10.1007/s11760‐020‐01644‐0 |
| [136] | CaoW, LuY, HeZ. Geometric algebra representation and ensemble action classification method for 3D skeleton orientation data. IEEE Access. 2019;7:13,2049‐13,2056. doi:10.1109/ACCESS.2019.2940291 |
| [137] | LiY, CaoW. An extended multilayer perceptron model using reduced geometric algebra. IEEE Access. 2019;7:129,815‐129,823. doi:10.1109/ACCESS.2019.2940217 |
| [138] | WangR, ShenM, WangX, et al. RGA‐CNNs: convolutional neural networks based on reduced geometric algebra. Sci China Inf Sci. 2021;64:129101. doi:10.1007/s11432‐018‐1513‐5 |
| [139] | WangR, XiaX, LiY, CaoW. Clifford fuzzy support vector machine for regression and its application in electric load forecasting of energy system. Front Energy Res. 2021;9:793078. doi:10.3389/fenrg.2021.793078 |
| [140] | LiY, WangX, HuoN. Weyl almost automorphic solutions in distribution sense of Clifford‐valued stochastic neural networks with time‐varying delays. Proc R Soc A Math Phys Eng Sci. 2022;478:2257. doi:10.1098/rspa.2021.0719 |
| [141] | PierdiccaR, PaolantiM, QuattriniR, MameliM, FrontoniE. A visual attentive model for discovering patterns in eye‐tracking data—a proposal in cultural heritage. Sensors. 2020;20(7):2101. doi:10.3390/s20072101 |
| [142] | Bayro‐CorrochanoE, Solis‐Gamboa S, Altamirano‐Escobedo G, Lechuga‐Gutierres L, Lisarraga‐Rodriguez J. Quaternion spiking and quaternion quantum neural networks: theory and applications. Int J Neural Syst. 2021;31(02):2050059. doi:10.1142/S0129065720500598 |
| [143] | Bayro‐CorrochanoE, Solis‐GamboaS, Quaternion quantum neurocomputing. Int J Wavelets Multiresolution Inf Process. 2020;18:2040001. Online Ready doi:10.1142/S0219691320400019 · Zbl 1492.81036 |
| [144] | RauARP. Symmetries and geometries of qubits, and their uses. Symmetry. 2021;13(9):1732. doi:10.3390/sym13091732 |
| [145] | WangY, ZhangF. An unified CGA‐based formal expression of spatio‐temporal topological relations for computation and analysis of geographic objects. AACA. 2019;29:59. doi:10.1007/s00006‐019‐0971‐2 · Zbl 1423.86003 |
| [146] | ShiZ, HuD, YinP, WangC, ChenT, ZhangJ. Calculation for multidimensional topological relations in 3D cadastre based on geometric algebra. ISPRS Int J Geo‐Inf. 2019;8(11):469. doi:10.3390/ijgi8110469 |
| [147] | ZhangJ, YinP, WangC, et al. 3D Topological Error Detection for Cadastral Parcels Based on Conformal Geometric Algebra. AACA. 2019;29:76. doi:10.1007/s00006‐019‐0994‐8 · Zbl 1422.91603 |
| [148] | BhattiUA, YuZ, YuanL, et al. Geometric Algebra Applications in Geospatial Artificial Intelligence and Remote Sensing Image Processing. IEEE Access. 2020;8:155,783‐155,796. doi:10.1109/ACCESS.2020.3018544 |
| [149] | BhattiUA, YuanL, YuZ, et al. Hybrid Watermarking algorithm using Clifford algebra with Arnold scrambling and chaotic encryption. IEEE Access. 2020;8:76,386‐76,398. doi:10.1109/ACCESS.2020.2988298 |
| [150] | BhattiUA, YuanL, YuZ, et al. New watermarking algorithm utilizing quaternion Fourier transform with advanced scrambling and secure encryption. Multimed Tools Appl. 2021;80:13,367‐13,387. doi:10.1007/s11042‐020‐10257���1 |
| [151] | LiuX, WuY, ZhangH, WuJ, ZhangL. Quaternion discrete fractional Krawtchouk transform and its application in color image encryption and watermarking. Signal Proc. 2021;189:108275. doi:10.1016/j.sigpro.2021.108275 |
| [152] | ChukanovSN. Transmission of geometric algebra encrypted signals,; 2020:25‐31. doi:10.17308/sait.2020.3/3037 |
| [153] | LavorC, Xambó‐DescampsS, ZaplanaI. A Geometric Algebra Invitation to Space‐Time Physics, Robotics and Molecular Geometry. New York: Springer; 2018. SpringerBriefs in Mathematics. · Zbl 1395.00007 |
| [154] | AlcerroL, RummelG. Aplicaciones de Algebra Geometrica en Relatividad Especial. Revista De La Escuela De Física. 2015;3(2):55‐57. doi:10.5377/ref.v3i2.8306 |
| [155] | WilsonJ, VisserM. Explicit Baker‐Campbell‐Hausdorff‐Dynkin formula for spacetime via geometric algebra. Int J Geom Methods Mod Phys. 2021;18(14):2150226. doi:10.1142/S0219887821502261 · Zbl 07838307 |
| [156] | HestenesD. Space Time Calculus. https://geocalc.clas.asu.edu/html/STC.html; 2020. |
| [157] | El HaouiY. Uncertainty principle for space‐time algebra‐valued functions. Mediterr J Math. 2021;18:97. doi:10.1007/s00009‐021‐01718‐4 · Zbl 1464.42009 |
| [158] | HitzerE. Quaternion and Clifford Fourier Transforms. London: Chapman and Hall/CRC; 2021. |
| [159] | HestenesD. Energy‐momentum complex in general relativity and gauge theory. AACA. 2021;31:51. doi:10.1007/s00006‐021‐01154‐3 · Zbl 1470.83026 |
| [160] | BarkerWEV, LasenbyAN, HobsonMP, HandleyWJ. Static energetics in gravity. J Math Phys. 2019;60:052504. doi:10.1063/1.5082730 · Zbl 1419.83026 |
| [161] | BarkerWEV, LasenbyAN, HobsonMP, HandleyWJ. Systematic study of background cosmology in unitary Poincaré gauge theories with application to emergent dark radiation and H0 tension. Phys Rev D. 2020;102:024048. doi:10.1103/PhysRevD.102.024048 |
| [162] | LasenbyAN. Geometric algebra, gravity and gravitational waves. AACA. 2019;29:79. doi:10.1007/s00006‐019‐0991‐y · Zbl 1429.83017 |
| [163] | AmbjornJ, WatabikiY. Models of the universe based on Jordan algebras. Nucl Phys B. 2020;955:115044. doi:10.1016/j.nuclphysb.2020.115044 · Zbl 1473.83081 |
| [164] | ArcodiaMRA, BelliniM. Fermionic origin of dark energy in the inflationary universe from unified spinor fields. Phys Scr. 2020;95:035303. doi:10.1088/1402‐4896/ab569f |
| [165] | Ten BoschM. N‐dimensional rigid body dynamics. ACM Trans Graph. 2020;39(4):55. doi:10.1145/3386569.3392483 |
| [166] | CakmakŞ, KilicA. The study of classics particles’ energy at Archimedian solids with Clifford algebra. Eskisehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering, Vol 20 ‐ ICONAT 2019 Special Issue. 2019:170‐180. doi:10.18038/estubtda.649511 |
| [167] | Moya‐SanchezEU, Maciel‐HernandezAM, NieblaAS, et al. Monte Carlo geometry modeling for particle transport using conformal geometric algebra. AACA. 2019;29:26. doi:10.1007/s00006‐019‐0939‐2 · Zbl 1412.65007 |
| [168] | Mathew PanakkalS, ParameswaranR, VedanMJ. A geometric algebraic approach to fluid dynamics. Phys Fluids. 2020;32:087111. doi:10.1063/5.0017344 |
| [169] | MoschandreouTE, AfasKC. Compressible Navier‐Stokes equations in cylindrical passages and general dynamics of surfaces‐(I)‐flow structures and (II)‐analyzing biomembranes under static and dynamic conditions. Mathematics. 2019;7(11):1060. doi:10.3390/math7111060 |
| [170] | MoschandreouTE. A Method of solving compressible Navier Stokes equations in cylindrical coordinates using geometric algebra. Mathematics. 2019;7(2):126. doi:10.3390/math7020126 |
| [171] | ÖzdemirZ, TuncerOO, GökI. Kinematic equations of Lorentzian magnetic flux tubes based on split quaternion algebra. Eur Phys J Plus. 2021;136:910. doi:10.1140/epjp/s13360‐021‐01893‐z |
| [172] | Prado OrbanX, MiraJ. Dimensional scaffolding of electromagnetism using geometric algebra. Eur J Phys. 2021;42(1):015204. doi:10.1088/1361‐6404/abaf62 · Zbl 1520.78008 |
| [173] | Romero‐RuizI, PousJ. The magnetotelluric impedance tensor through Clifford algebras: part I - theory. Geophys Prospect. 2019;67:651‐669. doi:10.1111/1365‐2478.12741 |
| [174] | ThiruvengadamS, MurphyM, MillerK. A Clifford algebra‐based mathematical model for the determination of critical temperatures in superconductors. J Math Chem. 2020;58:1926‐1986. doi:10.1007/s10910‐020‐01156‐9 · Zbl 1453.82095 |
| [175] | FisanovVV. Formulation of the Snell‐Descartes Laws in terms of geometric algebra. Russ Phys J. 2019;62:794‐799. doi:10.1007/s11182‐019‐01779‐9 · Zbl 1429.78001 |
| [176] | AmaoP, CastilloH. Two‐state quantum systems revisited: a Clifford algebra approach. AACA. 2021;31:23. doi:10.1007/s00006‐020‐01116‐1 · Zbl 1460.81118 |
| [177] | CamposAG, CabreraR. Nondispersive analytical solutions to the Dirac equation. Phys Rev Res. 2020;2:013051. doi:10.1103/physrevresearch.2.013051 |
| [178] | CamposAG, HatsagortsyanKZ, KeitelCH. Construction of Dirac spinors for electron vortex beams in background electromagnetic fields. Phys Rev Res. 2021;3:013245. doi:10.1103/physrevresearch.3.013245 |
| [179] | GutowskiJ, PapadopoulosG. Eigenvalue estimates for multi‐form modified Dirac operators. J Geom Phys. 2021;160:103954. doi:10.1016/j.geomphys.2020.103954 · Zbl 1459.35322 |
| [180] | AydemirU. Clifford‐based spectral action and renormalization group analysis of the gauge couplings. Eur Phys J C. 2019;79:325. doi:10.1140/epjc/s10052‐019‐6846‐9 |
| [181] | WolkBJ. The underlying geometry of the CAM gauge model of the standard model of particle physics. Int J Modern Phys A. 2020;35(07):2050037. doi:10.1142/S0217751X20500372 |
| [182] | BrannenC. Group geometric algebra and the standard model. J Mod Phys. 2020;11:1193‐1214. doi:10.4236/jmp.2020.118075 |
| [183] | MinU, SonM, Suh. HG. Group theoretic approach to fermion production. J High Energ Phys. 2019;72:2019. doi:10.1007/JHEP03(2019)072 · Zbl 1414.85012 |
| [184] | PetitjeanM. Chirality in geometric algebra. Mathematics. 2021;9(13):1521. doi:10.3390/math9131521 |
| [185] | McClellanGE. Using raising and lowering operators from geometric algebra for electroweak theory in particle physics. AACA. 2019;29:90. doi:10.1007/s00006‐019‐1002‐z · Zbl 1429.81105 |
| [186] | McClellanGE. Operators and field equations in the electroweak sector of particle physics. AACA. 2021;31:65. doi:10.1007/s00006‐021‐01168‐x · Zbl 07420427 |
| [187] | IgaK. Adinkras: graphs of Clifford algebra representations, supersymmetry, and codes. AACA. 2021;31:76. doi:10.1007/s00006‐021‐01181‐0 · Zbl 1478.15036 |
| [188] | HeldC. Quantum‐mechanical correlations and Tsirelson bound from geometric algebra. Quantum Stud Math Found. 2021;8:411‐417. doi:10.1007/s40509‐021‐00252‐y · Zbl 07899175 |
| [189] | LasenbyAN. A 1d up approach to conformal geometric algebra: applications in line fitting and quantum mechanics. AACA. 2020;30:22. doi:10.1007/s00006‐020‐1046‐0 · Zbl 1490.51020 |
| [190] | SoiguineA. Scattering of geometric algebra wave functions and collapse in measurements. J Appl Math Phys. 2020;8:1838‐1844. doi:10.4236/jamp.2020.89138 |
| [191] | SoiguineA. Instantly propagating states. J Appl Math Phys. 2021;9:468‐475. doi:10.4236/jamp.2021.93032 |
| [192] | ScanlonT, SverdlovR. Berezin integral as a limit of Riemann sum. J Math Phys. 2020;61:063505. doi:10.1063/1.5144877 · Zbl 1452.81135 |
| [193] | GreenwoodRN. On computable geometric expressions in quantum theory. AACA. 2020;30:7. doi:10.1007/s00006‐019‐1031‐7 · Zbl 1436.81022 |
| [194] | ShirokovDS. Calculation of elements of spin groups using method of averaging in Clifford’s geometric algebra. AACA. 2019;29:50. doi:10.1007/s00006‐019‐0967‐y · Zbl 1414.15028 |
| [195] | WangR, WangK, CaoW, WangX. Geometric algebra in signal and image processing: a survey. IEEE Access. 2019;7:156,315‐156,325. doi:10.1109/ACCESS.2019.2948615 |
| [196] | FranchiniS, GentileA, VassalloG, VitabileS. Implementation and evaluation of medical imaging techniques based on conformal geometric algebra. Int J Appl Math Comput Sci. 2020;30(3):415‐433. doi:10.34768/amcs‐2020‐0031 · Zbl 1466.92087 |
| [197] | VitabileS. Geometric calculus applications to medical imaging: status and perspectives. Systems, Patterns and Data Engineering with Geometric Calculi, SEMA SIMAI Springer Series. Cham, Switzerland: Springer; 2021:31‐46. doi:10.1007/978‐3‐030‐74486‐1_3 |
| [198] | YinX‐X, YinL, HadjiloucasS. Pattern classification approaches for breast cancer identification via MRI: state‐of‐the‐art and vision for the future. Appl Sci. 2020;10(20):7201. doi:10.3390/app10207201 |
| [199] | KhanPW, XuG, LatifMA, AbbasK, YasinA. UAV’s agricultural image segmentation predicated by Clifford geometric algebra. IEEE Access. 2019;7:38,442‐38,450. doi:10.1109/ACCESS.2019.2906033 |
| [200] | LiuY, ZhangS, LiG, et al. Accurate quaternion radial harmonic Fourier moments for color image reconstruction and object recognition. Pattern Anal Applic. 2020;23:1551‐1567. doi:10.1007/s10044‐020‐00877‐6 |
| [201] | KhanPW, ByunY‐C, LatifMA. Clifford geometric algebra‐based approach for 3D modeling of agricultural images acquired by UAVs. IEEE Access. 2020;8:226,297‐226,308. doi:10.1109/ACCESS.2020.3045443 |
| [202] | HitzerE, BengerW, NiederwieserM, et al. Foundations for strip adjustment of airborne laserscanning data with conformal geometric algebra. AACA. 2022;32:1. doi:10.1007/s00006‐021‐01184‐x · Zbl 1478.15035 |
| [203] | LianP. Sharp inequalities for geometric Fourier transform and associated ambiguity function. J Math Anal Appl. 2020;484(2):123730. doi:10.1016/j.jmaa.2019.123730 · Zbl 1452.42004 |
| [204] | LiY, JiangS. Multi‐focus image fusion using geometric algebra based discrete Fourier transform. IEEE Access. 2020;8:60,019‐60,028. doi:10.1109/ACCESS.2020.2981814 |
| [205] | ZhangL, SangY, DaiD. Accurate quaternion polar harmonic transform for color image analysis. Sci Program. 2021;7162779:9. doi:10.1155/2021/7162779 |
| [206] | OroujiN, SadrA. A hardware implementation for colour edge detection using Prewitt‐inspired filters based on geometric algebra. AACA. 2019;29:23. doi:10.1007/s00006‐019‐0941‐8 · Zbl 1442.68283 |
| [207] | LiY, LiQ, LiuY, XieW. A spatial‐spectral SIFT for hyperspectral image matching and classification. Pattern Recogn Lett. 2019;127:18‐26. doi:10.1016/j.patrec.2018.08.032 |
| [208] | HeB, LiuJ, YangT, et al. Quaternion fractional‐order color orthogonal moment‐based image representation and recognition. J Image Video Proc. 2021;2021:17. doi:10.1186/s13640‐021‐00553‐7 |
| [209] | WangR, ShenM, CaoW. Multivector sparse representation for multispectral images using geometric algebra. IEEE Access. 2019;7:12,755‐12,767. doi:10.1109/ACCESS.2019.2892822 |
| [210] | ShirokovDS. Basis‐free solution to Sylvester equation in Clifford algebra of arbitrary dimension. AACA. 2021;31:70. doi:10.1007/s00006‐021‐01173‐0 · Zbl 1476.15029 |
| [211] | WangR, ShenM, WangT, et al. AACA. 2019;29:33. doi:10.1007/s00006‐019‐0950‐7 |
| [212] | LiangH, WangJ, WangY, HuoW. Monocular‐vision‐based spacecraft relative state estimation under dual number algebra. Proceedings of the Institution of Mechanical Engineers. Part G: J Aerosp Eng. 2020;234(2):221‐235. doi:10.1177/0954410019864754 |
| [213] | LiY, LiQ, HuangQ, XiaR, LiX. Spatiotemporal interest point detector exploiting appearance and motion‐variation information. J Electron Imaging. 2019;28(3):033002. doi:10.1117/1.JEI.28.3.033002 |
| [214] | FangL, SunM. Motion recognition technology of badminton players in sports video images. Futur Gener Comput Syst. 2021;124:381‐389. doi:10.1016/j.future.2021.05.036 |
| [215] | WangR, WangY, LiY, CaoW, YanY. Geometric algebra‐based ESPRIT algorithm for DOA estimation. Sensors. 2021;21(17):5933. doi:10.3390/s21175933 |
| [216] | NittaT, KobayashiM, MandicDP. Hypercomplex widely linear estimation through the lens of underpinning geometry. IEEE Trans Signal Process. 2019;67(15):3985‐3994. doi:10.1109/TSP.2019.2922151 · Zbl 07123339 |
| [217] | LopesWB, LopesCG. Geometric‐algebra adaptive filters. IEEE Trans Signal Process. 2019;67(14):3649‐3662. doi:10.1109/TSP.2019.2916028 · Zbl 07123314 |
| [218] | WangH, HeY, LiY, WangR. An approach to adaptive filtering with variable step size based on geometric algebra. IET Commun. 2021:1‐12. doi:10.1049/cmu2.12188 |
| [219] | WangW, ZhaoH, ZengX. Geometric algebra correntropy: definition and application to robust adaptive filtering. IEEE Trans Circ Syst II: Express Briefs. 2020;67(6):1164‐1168. doi:10.1109/TCSII.2019.2931507 |
| [220] | RenY, ZhiY, ZhangJ. Geometric‐algebra affine projection adaptive filter. EURASIP J Adv Signal Process. 2021;82(2021):1‐13. doi:10.1186/s13634‐021‐00790‐y |
| [221] | HeY, WangR, WangX, ZhouJ, YanY. Novel adaptive filtering algorithms based on higher‐order statistics and geometric algebra. IEEE Access. 2020;8:73,767‐73,779. doi:10.1109/ACCESS.2020.2988521 |
| [222] | WangR, LiangM, HeY, WangX, CaoW. A normalized adaptive filtering algorithm based on geometric algebra. IEEE Access. 2020;8:92,861‐92,874. doi:10.1109/ACCESS.2020.2994230 |
| [223] | WangW, DogancayK. Transient performance analysis of geometric algebra least mean square adaptive filter. IEEE Trans Circ Syst II: Express Briefs. 2021;68(8):3027‐3031. doi:10.1109/TCSII.2021.3069390 |
| [224] | WangR, HeY, HuangC, WangX, CaoW. A novel least‐mean kurtosis adaptive filtering algorithm based on geometric algebra. IEEE Access. 2019;7:78,298‐78,310. DPO: doi:10.1109/ACCESS.2019.2922343 |
| [225] | LvS, ZhaoH, HeX. Geometric algebra based least mean m‐estimate robust adaptive filtering algorithm and its transient performance analysis. Signal Process. 2021;189:108235. doi:10.1016/j.sigpro.2021.108235 |
| [226] | WangW, WangJ. Convex combination of two geometric‐algebra least mean square algorithms and its performance analysis. Signal Proc. 2022;192:108333. doi:10.1016/j.sigpro.2021.108333 |
| [227] | WangR, ShiY, CaoW. GA‐SURF: A new speeded‐up robust feature extraction algorithm for multispectral images based on geometric algebra. Pattern Recogn Lett. 2019;127:11‐17. doi:10.1016/j.patrec.2018.11.001 |
| [228] | WangR, ZhangW, ShiY, WangX, CaoW. GA‐ORB: A new efficient feature extraction algorithm for multispectral images based on geometric algebra. IEEE Access. 2019;7:71,235‐71,244. doi:10.1109/ACCESS.2019.2918813 |
| [229] | YinP, ZhangJ, SunX, HuD, ShiZ, WuC. A vertex concavity‐convexity detection method for three‐dimensional spatial objects based on geometric algebra. ISPRS Int J Geo‐Inf. 2020;9(1):25. doi:10.3390/ijgi9010025 |
| [230] | SousaEV, FernandesLAF. TbGAL: a tensor‐based library for geometric algebra. AACA. 2020;30:27. doi:10.1007/s00006‐020‐1053‐1 · Zbl 1433.15004 |
| [231] | BreuilsS, NozickV, FuchsL. Garamon: a geometric algebra library generator. AACA. 2019;29:69. doi:10.1007/s00006‐019‐0987‐7 · Zbl 1422.68329 |
| [232] | JelinekA, LigockiA, ZaludL. Robotic template library. Journal of Open Research Software. 2021;9(1):25. doi:10.5334/jors.353 |
| [233] | AkarM. The essentials of clifford algebras with maple programming. Sakarya Univ J Sci. 2021;25(2):610‐618. |
| [234] | HildenbrandD, SteinmetzC, TichyR. GAALOPWeb for Matlab: an easy to handle solution for industrial geometric algebra implementations. AACA. 2020;30:52. doi:10.1007/s00006‐020‐01081‐9 · Zbl 1460.68132 |
| [235] | AlvesR, HildenbrandD, SteinmetzC, et al. Efficient development of competitive Mathematica solutions based on geometric algebra with GAALOPWeb. AACA. 2020;30:59. doi:10.1007/s00006‐020‐01085‐5 · Zbl 1457.68321 |
| [236] | EidAH. A low‐memory time‐efficient implementation of outermorphisms for higher‐dimensional geometric algebras. AACA. 2020;30:24. doi:10.1007/s00006‐020‐1047‐z · Zbl 1434.68703 |
| [237] | ChakrabortyA, BanerjeeA. Modular and parallel VLSI architecture of multi‐dimensional quad‐core GA co‐processor for real time image/video processing. Microprocess Microsyst. 2019;65:180‐195. doi:10.1016/j.micpro.2019.02.002 |
| [238] | AlvesR, HildenbrandD, HrdinaJ, et al. An online calculator for quantum computing operations based on geometric algebra. AACA. 2022;32(4):1‐20. doi:10.1007/s00006‐021‐01185‐w · Zbl 1533.68097 |
| [239] | HildenbrandD, FranchiniS, GentileA, VassalloG, VitabileS. GAPPCO: an easy to configure geometric algebra coprocessor based on GAPP programs. AACA; 27(3):2017. doi:10.1007/s00006‐016‐0755‐x · Zbl 1415.68267 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
