In this paper we investigate some well-established and more recent methods that aim at approximating the vector exp(A)v when A is a large symmetric negative semidefinite matrix, by efficiently combining subspace projections and spectral transformations. We show that some recently developed acceleration procedures may be restated as preconditioning techniques for the partial fraction expansion form of an approximating rational function. These new results allow us to devise a priori strategies to select the associated acceleration parameters; theoretical and numerical results are shown to justify these choices. Moreover, we provide a performance evaluation among several numerical approaches to approximate the action of the exponential of large matrices. Our numerical experiments provide a new, and in some cases, unexpected picture of the actual behavior of the discussed methods.

Acceleration Techniques for Approximating the Matrix Exponential Operator / Popolizio, M.; Simoncini, V.. - In: SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS. - ISSN 0895-4798. - STAMPA. - 30:2(2008), pp. 657-683. [10.1137/060672856]

Acceleration Techniques for Approximating the Matrix Exponential Operator

M. Popolizio;
2008-01-01

Abstract

In this paper we investigate some well-established and more recent methods that aim at approximating the vector exp(A)v when A is a large symmetric negative semidefinite matrix, by efficiently combining subspace projections and spectral transformations. We show that some recently developed acceleration procedures may be restated as preconditioning techniques for the partial fraction expansion form of an approximating rational function. These new results allow us to devise a priori strategies to select the associated acceleration parameters; theoretical and numerical results are shown to justify these choices. Moreover, we provide a performance evaluation among several numerical approaches to approximate the action of the exponential of large matrices. Our numerical experiments provide a new, and in some cases, unexpected picture of the actual behavior of the discussed methods.
2008
Acceleration Techniques for Approximating the Matrix Exponential Operator / Popolizio, M.; Simoncini, V.. - In: SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS. - ISSN 0895-4798. - STAMPA. - 30:2(2008), pp. 657-683. [10.1137/060672856]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/199905
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