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An iterative algorithm for the least squares bisymmetric solutions of the matrix equations

โœ Scribed by Jing Cai; Guoliang Chen

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
555 KB
Volume
50
Category
Article
ISSN
0895-7177

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โœฆ Synopsis

In this paper, an iterative algorithm is constructed to solve the minimum Frobenius norm residual problem: min

over bisymmetric matrices. By this algorithm, for any initial bisymmetric matrix X 0 , a solution X * can be obtained in finite iteration steps in the absence of roundoff errors, and the solution with least norm can be obtained by choosing a special kind of initial matrix. Furthermore, in the solution set of the above problem, the unique optimal approximation solution X to a given matrix X in the Frobenius norm can be derived by finding the least norm bisymmetric solution of a new corresponding minimum Frobenius norm problem. Given numerical examples show that the iterative algorithm is quite effective in actual computation.

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