Year: 2005
Journal of Computational Mathematics, Vol. 23 (2005), Iss. 1 : pp. 17–26
Abstract
By making use of the quotient singular value decomposition (QSVD) of a matrix pair, this paper establishes the necessary and sufficient conditions for the existence of and the expressions for the general solutions of the linear matrix equation $AXA^T+BYB^T=C$ with the unknown $X$ and $Y$, which may be both symmetric, skew-symmetric, nonnegative definite , positive definite or some cross combinations respectively. Also, the solutions of some optimal problems are derived.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2005-JCM-8792
Journal of Computational Mathematics, Vol. 23 (2005), Iss. 1 : pp. 17–26
Published online: 2005-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Matrix equation Matrix norm QSVD Constrained condition Optimal problem.