Computation of a function of a matrix with close eigenvalues by means of the Newton interpolating polynomial
Numerical Analysis
2023-12-13 v1 Numerical Analysis
Classical Analysis and ODEs
Dynamical Systems
Spectral Theory
Abstract
An algorithm for computing an analytic function of a matrix is described. The algorithm is intended for the case where has some close eigenvalues, and clusters (subsets) of close eigenvalues are separated from each other. This algorithm is a modification of some well known and widely used algorithms. A novel feature is an approximate calculation of divided differences for the Newton interpolating polynomial in a special way. This modification does not require to reorder the Schur triangular form and to solve Sylvester equations.
Keywords
Cite
@article{arxiv.1402.4003,
title = {Computation of a function of a matrix with close eigenvalues by means of the Newton interpolating polynomial},
author = {V. G. Kurbatov and I. V. Kurbatova},
journal= {arXiv preprint arXiv:1402.4003},
year = {2023}
}
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11 pages