An Iterative Algorithm for the Least Squares Generalized Reflexive Solutions of the Matrix Equations AXB = E,CXD = F

Feng Yin and Guang-Xin Huang

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: 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: ∥(AXBCXD)-(EF)∥= min over generalized reflexive matrix X. For any initial generalized reflexive matrix X1, by the iterative algorithm, the generalized reflexive solution X* can be obtained within finite iterative steps in the absence of round‐off errors, and the unique least‐norm generalized reflexive solution X* can also be derived when an appropriate initial iterative matrix is chosen. Furthermore, the unique optimal approximate solution X∧ to a given matrix X0 in Frobenius norm can be derived by finding the least‐norm generalized reflexive solution X~* of a new corresponding minimum Frobenius norm residual problem: min∥(AX~BCX~D)-(E~F~)∥ with E~=E-AX0B, F~=F-CX0D. Finally, several numerical examples are given to illustrate that our iterative algorithm is effective.

Date: 2012
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2012/857284

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:857284

Access Statistics for this article

More articles in Abstract and Applied Analysis from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().