1. Sherman–Morrison–Woodbury formula for Sylvester and T -Sylvester equations with applications.
- Author
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Kuzmanović, Ivana and Truhar, Ninoslav
- Subjects
- *
SHERMAN-Morrison-Woodbury formula , *NUMERICAL solutions to equations , *MATRICES (Mathematics) , *NUMERICAL calculations , *NUMERICAL analysis , *MATHEMATICAL analysis , *OPERATOR theory - 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]
- Published
- 2013
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