The iterative solution of the matrix equation \(XA+BX+C=0\)

DOI10.1016/0024-3795(88)90008-0zbMath0663.65032OpenAlexW2004054427MaRDI QIDQ1114306

David F. Miller

Publication date: 1988

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(88)90008-0

zbMATH Keywords

stabilityconvergenceLyapunov equationiterative algorithmsmatrix polynomiallinear matrix equation

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Discrete-time control/observation systems (93C55) Matrix equations and identities (15A24) Iterative numerical methods for linear systems (65F10)

Related Items (6)

On Smith-type iterative algorithms for the Stein matrix equation ⋮ Parametric Solutions to the Generalized Discrete Yakubovich-Transpose Matrix Equation ⋮ Closed-form solutions to the nonhomogeneous Yakubovich-transpose matrix equation ⋮ Toward solution of matrix equation \(X=Af(X)B+C\) ⋮ On the equivalence of the operator equations \(XA+BX=C\) and \(X-p(- B)Xp(A)^{-1}=W\) in a Hilbert space, p a polynomial ⋮ Extension of the Barzilai–Borwein Method for Quadratic Forms in Finite Euclidean Spaces

Uses Software

• Algorithm 432

Cites Work

• Numerical solution of \(A^ tS + SA + Q = 0\).
• A Hessenberg-Schur method for the problem AX + XB= C
• The numerical solution of<tex>A'Q+QA = -C</tex>
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• Matrix Equation $XA + BX = C$
• Explicit Solutions of Linear Matrix Equations

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