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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De Gruyter
2017-01-01
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| Series: | Special Matrices |
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| 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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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 |
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| 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 |
| _version_ |
1612671629172670464 |