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

MSC:
65F10Iterative methods for linear systems
65F30Other matrix algorithms
15A24Matrix equations and identities