Estimates of the trace of the inverse of a symmetric matrix using the modified Chebyshev algorithm

In this paper we study how to compute an estimate of the trace of the inverse of a symmetric matrix by using Gauss quadrature and the modified Chebyshev algorithm. As auxiliary polynomials we use the shifted Chebyshev polynomials. Since this can be too costly in computer storage for large matrices w...

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Bibliographic Details
Published in:Numerical algorithms Vol. 51; no. 3; pp. 309 - 318
Main Author: Meurant, Gérard
Format: Journal Article
Language:English
Published: Boston Springer US 01.07.2009
Springer Nature B.V
Subjects:
Algebra
Algorithms
Chebyshev approximation
Computer Science
Computer simulation
Estimates
Inverse
Mathematical analysis
Matrices (mathematics)
Numeric Computing
Numerical Analysis
Original Paper
Polynomials
Quadratures
Symmetry
Theory of Computation
Trace
Inverse
Chebyshev algorithm
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:In this paper we study how to compute an estimate of the trace of the inverse of a symmetric matrix by using Gauss quadrature and the modified Chebyshev algorithm. As auxiliary polynomials we use the shifted Chebyshev polynomials. Since this can be too costly in computer storage for large matrices we also propose to compute the modified moments with a stochastic approach due to Hutchinson (Commun Stat Simul 18:1059–1076, 1989 ).
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-008-9246-z