An Iterative Algorithm for the Least Squares Generalized Reflexive Solutions of the Matrix Equations | Zendy

Feng Yin | Zendy; Guang-Xin Huang | Zendy

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An Iterative Algorithm for the Least Squares Generalized Reflexive Solutions of the Matrix Equations

Author(s) -

Feng Yin,

Guang-Xin Huang

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/857284

Subject(s) - mathematics , sylvester matrix , iterative method , matrix norm , norm (philosophy) , residual , matrix (chemical analysis) , matrix splitting , algebra over a field , mathematical optimization , algorithm , pure mathematics , state transition matrix , symmetric matrix , mathematical analysis , eigenvalues and eigenvectors , polynomial matrix , physics , materials science , matrix polynomial , quantum mechanics , political science , polynomial , law , composite material

The generalized coupled Sylvester systems play a fundamental role in wide applications in several areas, such as stability theory, control theory, perturbation analysis, and some other fields of pure and applied mathematics. The iterative method is an important way to solve the generalized coupled Sylvester systems. In this paper, an iterative algorithm is constructed to solve the minimum Frobenius norm residual problem: ‖−‖= min over generalized reflexive matrix . For any initial generalized reflexive matrix 1, by the iterative algorithm, the generalized reflexive solution ∗ can be obtained within finite iterative steps in the absence of round-off errors, and the unique least-norm generalized reflexive solution ∗ can also be derived when an appropriate initial iterative matrix is chosen. Furthermore, the unique optimal approximate solution to a given matrix 0 in Frobenius norm can be derived by finding the least-norm generalized reflexive solution ∗ of a new corresponding minimum Frobenius norm residual problem: min‖−‖ with =−0, =−0. Finally, several numerical examples are given to illustrate that our iterative algorithm is effective

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