The matrix equation \(X + AX^TB = C\): Conditions for unique solvability and a numerical algorithm for its solution

DOI10.1134/S1064562412020299zbMath1255.15021OpenAlexW2075939902MaRDI QIDQ1760997

Yu. O. Vorontsov, Khakim D. Ikramov

Publication date: 15 November 2012

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562412020299

zbMATH Keywords

algorithmmatrix equation

Mathematics Subject Classification ID

Related Items (9)

The matrix equations \(AX+BX^T=C\) and \(AX+BX^\ast=C\) ⋮ Numerical solution of the matrix equation X — $A\bar XB$ = C in the self-adjoint case ⋮ Numerical solution of matrix equations of the Stein type in the self-adjoint case ⋮ Uniqueness of solution of a generalized \(\star\)-Sylvester matrix equation ⋮ Numerical algorithms for solving matrix equations AX + BX T = C and AX + BX* = C ⋮ Modifying a numerical algorithm for solving the matrix equation X + AX T B = C ⋮ Restarted global FOM and GMRES algorithms for the Stein-like matrix equation \(X + \mathcal{M}(X) = C\) ⋮ A note on the \(\top\)-Stein matrix equation ⋮ Numerical solution of matrix equations of the form X + AX T B = C

Cites Work

• Toward solution of matrix equation \(X=Af(X)B+C\)
• Conditions for unique solvability of the matrix equation \(AX + X^TB = C\)
• On the unique solvability of the matrix equation \(AX + X^{T}B = C\) in the singular case
• The periodic QR algorithm is a disguised QR algorithm
• A numerical algorithm for solving the matrix equation AX + X T B = C 1

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