2006•Journal of Northwest UniversityRequires access

On parameter iterative method for solving matrix equation AXB+CXD=F

Cai Yuan-hu

Abstract

Aim To construct the parameter iterative method for solving large matrix equation AXB+CXD=F which has a unique solution.Methods The matrix transformation method and matrix eigenvalue analysis method.Results The equivalent matrix equation is derived by the matrix transformation method.The parameter iterative algorithm and the sufficient and necessary conditions for the convergence are given.When A,B,C and D are positive definite Hermitian matrices,the formulas are presented to compute the optimal parameter and the approximate optimal parameter.Conclusion The parameter iterative method for solving large matrix equation AXB+CXD=F is proposed when it has a unique solution.The convergence theorem of the parameter iterative algorithm is proved.Moreover the existence theorem of the optimal parameter is also proved under mild conditions.

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Key concepts: Iterative method, Matrix (chemical analysis), Applied mathematics, Convergence (economics), Eigenvalues and eigenvectors, Convergent matrix, Mathematics, Transformation (genetics)