On iterative solutions of general coupled matrix equations. (English) Zbl 1115.65035

Ding, Feng; Chen, Tongwen

SIAM J. Control Optim. 44, No. 6, 2269-2284 (2006).

The paper is focused on numerical solutions using the Jacobi and Gauss-Seidel iterations of coupled Sylvester matrix equations as well as general coupled matrix equations. Gradient-based iterative algorithms are presented by using the gradient search principle and the hierarchical identification principle. It is proved that the proposed gradient iterative algorithm solving a more general coupled matrix equation always converges to the (unique) solution for any initial value. The algorithm is based on a block-matrix inner product – the star product. Two numerical examples are supplied.

Reviewer: Lubomír Bakule (Praha)

MSC:

65F10	Iterative numerical methods for linear systems
65F30	Other matrix algorithms (MSC2010)
15A24	Matrix equations and identities

Keywords:

Matrix equations; gradient search principle; Jacobi and Gauss-Seidel iterations; Hadamard and star products; hierarchical identification principle