Abstract
An algorithm of the Bartels-Stewart type for solving the matrix equation AX + X*B = C is suggested. By applying the QZ-algorithm to the original equation, it is transformed into an equation of the same type with triangular matrix coefficients A and B. The resulting matrix equation is equivalent to the sequence of a system of linear equations with a smaller order of the coefficients of the desired solution. Using numerical examples, the authors simulate a situation where the conditions of a unique solution are “almost” violated. Deterioration of the calculated solutions is in this case followed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
F. R. Gantmacher, The Theory of Matrices (Nauka, Moscow, 1966; Chelsea, New York, 1959).
Kh. D. Ikramov, Numerical Solution of Matrix Equations (Nauka, Moscow, 1984) [in Russian].
Yu. O. Vorontsov and Kh. D. Ikramov, “Conditions for Unique Solvability of the Matrix Equation AX + X*B = C,” Comp. Math. Math. Phys. 52, 665–673 (2012).
Kh. D. Ikramov, “Conditions for Unique Solvability of the Matrix Equation AX + XTB = C,” Dokl. Math. 81, 63–65 (2010).
Kh. D. Ikramov and Yu. O. Vorontsov, “A Numerical Algorithm for Solving the Matrix Equation AX + XTB = C,” Comp. Math. Math. Phys. 51, 691–699 (2011).
Kh. D. Ikramov and Yu. O. Vorontsov, “On the Unique Solvability of the Matrix Equation AX + XTB = C in the Singular Case,” Dokl. Math. 83, 380–383 (2011).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © Yu.O. Vorontsov, 2013, published in Vestnik Moskovskogo Universiteta. Vychislitel’naya Matematika i Kibernetika, 2013, No. 1, pp. 3–9.
About this article
Cite this article
Vorontsov, Y.O. Numerical algorithm for solving the matrix equation AX + X* B = C . MoscowUniv.Comput.Math.Cybern. 37, 1–7 (2013). https://doi.org/10.3103/S0278641913010068
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0278641913010068