Name
Abstract | ||
|---|---|---|
This paper presents an iterative method for solving the matrix equation AXB + CYD = E with real matrices X and Y. By this iterative method, the solvability of the matrix equation can be determined automatically. And when the matrix equation is consistent, then, for any initial matrix pair [X-o, Y-o], a solution pair can be obtained within finite iteration steps in the absence of round-off errors, and the least norm solution pair can be obtained by choosing a special kind of initial matrix pair. Furthermore, the optimal approximation solution pair to a given matrix pair [(X) over bar, (Y) over bar] in a Frobenius norm can be obtained by finding the least norm solution pair of a new matrix equation A (X) over tildeB + C (Y) over tildeD = (E) over tilde, where (E) over tilde = E - A (X) over barB - C (Y) over barD. The given numerical examples show that the iterative method is efficient. Copyright (C) 2005 John Wiley & Sons, Ltd. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1002/nla.470 | NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS |
Keywords | Field | DocType |
iterative method,matrix equation,matrix nearness problem,least-norm solution,optimal approximation solution | Convergent matrix,Mathematical optimization,Nonnegative matrix,Mathematical analysis,Matrix difference equation,Matrix function,Symmetric matrix,Matrix splitting,Centrosymmetric matrix,Mathematics,Block matrix | Journal |
Volume | Issue | ISSN |
13 | 6 | 1070-5325 |
Citations | PageRank | References |
19 | 2.14 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zhenyun Peng | 1 | 126 | 24.44 |
| Yaxin Peng | 2 | 73 | 16.82 |