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Gu, Chao; Wang, Jue Yu; Zhu, De Tong

An inexact Newton-Lanczos method for solving a system of nonlinear equations. (Chinese. English summary) Zbl 07828152

Acta Math. Sin., Chin. Ser. 66, No. 2, 317-338 (2023).
Summary: We present an inexact Newton-Krylov subspace method with incomplete line search technique for solving symmetric nonlinear equations, in which the Krylov subspace method uses the Lanczos-type decomposition technique. The iterative direction is obtained by approximately solving the Newton’s equations of the nonlinear equations using the Lanczos method. The global convergence and local superlinear convergence rate of the proposed algorithm are established under some reasonable conditions. Finally, the numerical results show the effectiveness of the proposed algorithm.

MSC:

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming

Keywords:

inexact-Newton method; Newton-Krylov subspace method; Lanczos method; symmetric nonlinear equations; global convergence
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References:

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