Fast algorithms for the Sylvester equation \(AX-XB^{T}=C\)

DOI10.1016/S0304-3975(00)00322-4zbMath0972.68183MaRDI QIDQ5941297

Peter Kirrinnis

Publication date: 20 August 2001

Published in: Theoretical Computer Science (Search for Journal in Brave)

zbMATH Keywords

fast algorithmsmatrix equationsalgebraic complexitySylvester equation

Mathematics Subject Classification ID

Nonnumerical algorithms (68W05)

Related Items (12)

Explicit solution of the operator equation \(A^{*}X+X^{*}A=B\) ⋮ Two algorithms for finding the Hermitian reflexive and skew-Hermitian solutions of Sylvester matrix equations ⋮ Analysis of an iterative algorithm to solve the generalized coupled Sylvester matrix equations ⋮ A Geometric Approach to Dynamical Model Order Reduction ⋮ An iterative algorithm for the reflexive solutions of the generalized coupled Sylvester matrix equations and its optimal approximation ⋮ Operator equations and inner inverses of elementary operators ⋮ On the reflexive and anti-reflexive solutions of the generalised coupled Sylvester matrix equations ⋮ A preconditioned iteration method for solving Sylvester equations ⋮ The solution to matrix equation \(AX+X^TC=B\) ⋮ Solutions of the Sylvester equation in \(C^*\)-modular operators ⋮ On the generalized bisymmetric and skew-symmetric solutions of the system of generalized Sylvester matrix equations ⋮ Free (rational) derivation

Uses Software

• LAPACK
• mctoolbox
• RICPAC
• Algorithm 432

Cites Work

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• Matrix multiplication via arithmetic progressions
• Fast algorithms for the characteristic polynomial
• Three methods for refining estimates of invariant subspaces
• SOR for \(AX-XB=C\)
• Fast rectangular matrix multiplication and applications
• Rectangular matrix multiplication revisited
• Gaussian elimination is not optimal
• On the computational power of pushdown automata
• On multiplication of 2 \(\times\) 2 matrices
• Matrix Analysis
• A Hessenberg-Schur method for the problem AX + XB= C
• Exploiting fast matrix multiplication within the level 3 BLAS
• Nearly Optimal Algorithms for Canonical Matrix Forms
• An Efficient Formula for Linear Recurrences
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]

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