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Least-Squares Solution with the Minimum-Norm for the Matrix Equation A T XB+B T X T A = D and Its Applications

Least-Squares Solution with the Minimum-Norm for the Matrix Equation A T XB+B T X T A = D... An efficient method based on the projection theorem, the generalized singular value decomposition and the canonical correlation decomposition is presented to find the least-squares solution with the minimum-norm for the matrix equation A T XB+B T X T A = D. Analytical solution to the matrix equation is also derived. Furthermore, we apply this result to determine the least-squares symmetric and sub-antisymmetric solution of the matrix equation C T XC = D with minimum-norm. Finally, some numerical results are reported to support the theories established in this paper. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Least-Squares Solution with the Minimum-Norm for the Matrix Equation A T XB+B T X T A = D and Its Applications

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Publisher
Springer Journals
Copyright
Copyright © 2007 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-007-0369-0
Publisher site
See Article on Publisher Site

Abstract

An efficient method based on the projection theorem, the generalized singular value decomposition and the canonical correlation decomposition is presented to find the least-squares solution with the minimum-norm for the matrix equation A T XB+B T X T A = D. Analytical solution to the matrix equation is also derived. Furthermore, we apply this result to determine the least-squares symmetric and sub-antisymmetric solution of the matrix equation C T XC = D with minimum-norm. Finally, some numerical results are reported to support the theories established in this paper.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jan 1, 2007

References