Generalized matrix functions were first introduced in [J. B. Hawkins and A. Ben-Israel, Linear and Multilinear Algebra, 1(2), 1973, pp. 163-171]. Recently, it has been recognized that these matrix functions arise in a number of applications, and various numerical methods have been proposed for their computation. The exploitation of structural properties, when present, can lead to more efficient and accurate algorithms. The main goal of this paper is to identify structural properties of matrices which are preserved by generalized matrix functions. In cases where a given property is not preserved in general, we provide conditions on the underlying scalar function under which the property of interest will be preserved by the corresponding generalized matrix function.

Some matrix properties preserved by generalized matrix functions

Benzi, Michele
;
2019

Abstract

Generalized matrix functions were first introduced in [J. B. Hawkins and A. Ben-Israel, Linear and Multilinear Algebra, 1(2), 1973, pp. 163-171]. Recently, it has been recognized that these matrix functions arise in a number of applications, and various numerical methods have been proposed for their computation. The exploitation of structural properties, when present, can lead to more efficient and accurate algorithms. The main goal of this paper is to identify structural properties of matrices which are preserved by generalized matrix functions. In cases where a given property is not preserved in general, we provide conditions on the underlying scalar function under which the property of interest will be preserved by the corresponding generalized matrix function.
2019
Settore MAT/08 - Analisi Numerica
generalized matrix functions; structure preservation; structured matrices; Algebra and Number Theory; Geometry and Topology
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/75984
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