English

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 AA is described. The algorithm is intended for the case where AA 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