Computation of a function of a matrix with close eigenvalues by means of the Newton interpolating polynomial

2014/02/17 by V. G. Kurbatov, Kurbatov, V. G., И. В. Курбатова +1
Computer Science · Mathematics · Physics and Astronomy · #65F60 41A10 65D05 #Advanced Optimization Algorithms Research #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #G.1.3 #Matrix Theory and Algorithms #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1402.4003

openalex publication_date 2014/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An algorithm for computing an analytic function of a matrix A is described. The algorithm is intended for the case where A 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.

Citations

• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later

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