Some important applicative problems require the evaluation of functions of large and sparse and/or localized matrices A. Popular and interesting techniques for computing (A) and (A)v, where v is a vector, are based on partial fraction expansions. However, some of these techniques require solving several linear systems whose matrices differ from A by a complex multiple of the identity matrix I for computing (A)v or require inverting sequences of matrices with the same characteristics for computing (A). Here we study the use and the convergence of a recent technique for generating sequences of incomplete factorizations of matrices in order to face with both these issues. The solution of the sequences of linear systems and approximate matrix inversions above can be computed efficiently provided that A−1 shows certain decay properties. These strategies have good parallel potentialities. Our claims are confirmed by numerical tests.

Bertaccini, D., Popolizio, M., Durastante, F. (2019). Efficient approximation of functions of some large matrices by partial fraction expansions. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 96(9), 1799-1817 [10.1080/00207160.2018.1533123].

Efficient approximation of functions of some large matrices by partial fraction expansions

Bertaccini, D.
;
2019-01-01

Abstract

Some important applicative problems require the evaluation of functions of large and sparse and/or localized matrices A. Popular and interesting techniques for computing (A) and (A)v, where v is a vector, are based on partial fraction expansions. However, some of these techniques require solving several linear systems whose matrices differ from A by a complex multiple of the identity matrix I for computing (A)v or require inverting sequences of matrices with the same characteristics for computing (A). Here we study the use and the convergence of a recent technique for generating sequences of incomplete factorizations of matrices in order to face with both these issues. The solution of the sequences of linear systems and approximate matrix inversions above can be computed efficiently provided that A−1 shows certain decay properties. These strategies have good parallel potentialities. Our claims are confirmed by numerical tests.
2019
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/08 - ANALISI NUMERICA
English
Bertaccini, D., Popolizio, M., Durastante, F. (2019). Efficient approximation of functions of some large matrices by partial fraction expansions. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 96(9), 1799-1817 [10.1080/00207160.2018.1533123].
Bertaccini, D; Popolizio, M; Durastante, F
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/215046
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