New block quadrature rules for the approximation of matrix functions. (English) Zbl 1338.65122
Summary: Golub and Meurant have shown how to use the symmetric block Lanczos algorithm to compute block Gauss quadrature rules for the approximation of certain matrix functions. We describe new block quadrature rules that can be computed by the symmetric or nonsymmetric block Lanczos algorithms and yield higher accuracy than standard block Gauss rules after the same number of steps of the symmetric or nonsymmetric block Lanczos algorithms. The new rules are block generalizations of the generalized averaged Gauss rules introduced by Spalević. Applications to network analysis are presented.
MSC:
| 65F60 | Numerical computation of matrix exponential and similar matrix functions |
| 65D32 | Numerical quadrature and cubature formulas |
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
| 05C82 | Small world graphs, complex networks (graph-theoretic aspects) |
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