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1. A Hessenberg method for the numerical solutions to types of block Sylvester matrix equations

Author

Ramadan, Mohamed A., El-Shazly, Naglaa M., and Selim, Basem I.

Subjects
*NUMERICAL solutions to equations, *SIMILARITY transformations, *LINEAR systems, *NUMERICAL analysis, *ORTHOGONALIZATION, *POINT mappings (Mathematics)
Abstract

Abstract: In this paper, we propose a new algorithm to solve the Sylvester matrix equation . The technique consists of orthogonal reduction of the matrix to a block upper Hessenberg form and then solving the reduced equation, for through recurrence relation, where , and . We then recover the solution of the original problem via the relation . The numerical results show the accuracy and the efficiency of the proposed algorithm. In addition, how the technique described can be applied to other matrix equations was shown. [Copyright &y& Elsevier]

Published
2010
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