This article is cited in 3 papers

Numerical algorithms for solving matrix equations $AX+BX^T=C$ and $AX+BX^*=C$

Yu. O. Vorontsov, Khakim D. Ikramov

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: Conditions for the unique solvability of matrix equations of the form $AX+BX^T=C$ and $AX+BX^*=C$ are found. Numerical algorithms of the Bartels–Stewart type for solving such equations are described. Certain numerical tests with these algorithms are presented. In particular, the situation where the conditions for unique solvability are “almost” violated is modeled, and the deterioration of the quality of the computed solution in this situation is traced through.

Key words: matrix equation, adjoint operator, QZ algorithm, matrix pencil, eigenvalue, circulant.

UDC: 519.6

Received: 24.12.2012

DOI: 10.7868/S0044466913060239

 English version: Computational Mathematics and Mathematical Physics, 2013, 53:6, 667–676

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