An effective recursive formula for the Frobenius covariants in matrix functions

For theoretical studies, it is helpful to have an explicit expression for a matrix function. Several methods have been used to determine the required Frobenius covariants. This paper presents a recursive formula that calculates these covariants effectively. The new aspect of this method is the simpl...

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Main Author: Schäfer F.
Format: Article
Language:English
Published: De Gruyter 2017-01-01
Series:Special Matrices
Subjects:
Online Access:http://www.degruyter.com/view/j/spma.2017.5.issue-1/spma-2017-0012/spma-2017-0012.xml?format=INT
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spelling doaj-art-66f93ab70dbc4e918b78fd904dfe97802018-08-24T19:57:01ZengDe GruyterSpecial Matrices2300-74512017-01-015111312210.1515/spma-2017-0012spma-2017-0012An effective recursive formula for the Frobenius covariants in matrix functionsSchäfer F.0Institute for Mathematics, University of Klagenfurt, 9020 Klagenfurt, AustriaFor theoretical studies, it is helpful to have an explicit expression for a matrix function. Several methods have been used to determine the required Frobenius covariants. This paper presents a recursive formula that calculates these covariants effectively. The new aspect of this method is the simple determination of the occurring coefficients in the covariants. The advantage is shown by several examples for the matrix exponential in comparision with Mathematica. The calculations are performed exactly.http://www.degruyter.com/view/j/spma.2017.5.issue-1/spma-2017-0012/spma-2017-0012.xml?format=INTmatrix functionFrobenius covariantsconstituent matricesPrimary 15A16Secondary 65F60
institution Open Data Bank
collection Open Access Journals
building Directory of Open Access Journals
language English
format Article
author Schäfer F.
spellingShingle Schäfer F.
An effective recursive formula for the Frobenius covariants in matrix functions
Special Matrices
matrix function
Frobenius covariants
constituent matrices
Primary 15A16
Secondary 65F60
author_facet Schäfer F.
author_sort Schäfer F.
title An effective recursive formula for the Frobenius covariants in matrix functions
title_short An effective recursive formula for the Frobenius covariants in matrix functions
title_full An effective recursive formula for the Frobenius covariants in matrix functions
title_fullStr An effective recursive formula for the Frobenius covariants in matrix functions
title_full_unstemmed An effective recursive formula for the Frobenius covariants in matrix functions
title_sort effective recursive formula for the frobenius covariants in matrix functions
publisher De Gruyter
series Special Matrices
issn 2300-7451
publishDate 2017-01-01
description For theoretical studies, it is helpful to have an explicit expression for a matrix function. Several methods have been used to determine the required Frobenius covariants. This paper presents a recursive formula that calculates these covariants effectively. The new aspect of this method is the simple determination of the occurring coefficients in the covariants. The advantage is shown by several examples for the matrix exponential in comparision with Mathematica. The calculations are performed exactly.
topic matrix function
Frobenius covariants
constituent matrices
Primary 15A16
Secondary 65F60
url http://www.degruyter.com/view/j/spma.2017.5.issue-1/spma-2017-0012/spma-2017-0012.xml?format=INT
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