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

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...

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Bibliographic Details
Published in:Linear & multilinear algebra Vol. 64; no. 2; pp. 111 - 122
Main Authors: Kurbatov, V.G., Kurbatova, I.V.
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 01.02.2016
Taylor & Francis Ltd
Subjects:
Algorithms
Approximation
Clusters
Computation
Eigenvalues
impulse response
Mathematical analysis
matrix exponential
matrix function
Newton interpolating polynomial
Polynomials
Schur decomposition
ISSN:0308-1087, 1563-5139
Online Access:Get full text
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Summary: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.
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ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2015.1024243