An iterative method for the least squares solution with the minimum norm of Sylvester matrix equation. (Chinese. English summary) Zbl 1299.65084
Summary: The Sylvester matrix equation \(AX+YB=C\) with two unknown matrices \(X, Y\) is discussed. By applying a hierarchical identification principle, we propose an iterative algorithm for solving the least norm problem of the equation. We prove that the iterative solution converges to the least-squares solution and the least-squares solution with the minimum norm for some initial values. Furthermore, the iterative method is extended to solve the least Frobenius norm problem of a general matrix equation. Finally, the algorithm is tested on a computer and the results verify the theoretical findings.
MSC:
65F30 | Other matrix algorithms (MSC2010) |
65F10 | Iterative numerical methods for linear systems |
15A24 | Matrix equations and identities |
65F20 | Numerical solutions to overdetermined systems, pseudoinverses |