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Sherman–Morrison–Woodbury formula for Sylvester and T -Sylvester equations with applications.
- Source :
-
International Journal of Computer Mathematics . Feb2013, Vol. 90 Issue 2, p306-324. 19p. 1 Diagram, 3 Charts, 3 Graphs. - Publication Year :
- 2013
-
Abstract
- In this paper, we present the Sherman–Morrison–Woodbury-type formula for the solution of the Sylvester equation of the formas well as for the solution of theT-Sylvester equation of the formwhereU1,U2,V1,V2are low-rank matrices. Although the matrix version of this formula for the Sylvester equation has been used in several different applications (but not for the case of aT-Sylvester equation), we present a novel approach using a proper operator representation. This novel approach allows us to derive a matrix version of the Sherman–Morrison–Woodbury-type formula for the Sylvester equation as well as for theT-Sylvester equation which seems to be new. We also present algorithms for the efficient calculation of the solution of structured Sylvester andT-Sylvester equations by using these formulas and illustrate their application in several examples. [ABSTRACT FROM PUBLISHER]
Details
- Language :
- English
- ISSN :
- 00207160
- Volume :
- 90
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- International Journal of Computer Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 85161008
- Full Text :
- https://doi.org/10.1080/00207160.2012.716154