Trail to a Lyapunov equation solver

DOI10.1016/j.camwa.2007.04.048zbMath1139.65033OpenAlexW2077976504MaRDI QIDQ2425443

Eugene L. Wachspress

Publication date: 5 May 2008

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2007.04.048

zbMATH Keywords

algorithmLyapunov matrix equationLanczos algorithmmatrix decompositionSylvester matrix equationlow rankalternating direction implicit (ADI) iterative solution

Mathematics Subject Classification ID

Related Items (4)

Wasserstein Riemannian geometry of Gaussian densities ⋮ Analysis of the solution of the Sylvester equation using low-rank ADI with exact shifts ⋮ Bounds on the Singular Values of Matrices with Displacement Structure ⋮ On the ADI method for Sylvester equations

Uses Software

• Algorithm 432

Cites Work

• Solution of Lyapunov equations by alternating direction implicit iteration
• Generalized ADI preconditioning
• Iterative solution of the Lyapunov matrix equation
• The ADI minimax problem for complex spectra
• The Tchebychev iteration for nonsymmetric linear systems
• The Numerical Solution of Parabolic and Elliptic Differential Equations
• Optimum Alternating-Direction-Implicit Iteration Parameters for a Model Problem
• A Hessenberg-Schur method for the problem AX + XB= C
• Numerical Solution of the Stable, Non-negative Definite Lyapunov Equation Lyapunov Equation
• Alternating Direction Implicit Iteration for Systems with Complex Spectra
• Optimal Alternating Direction Implicit Parameters for Nonsymmetric Systems of Linear Equations
• On the Third and Fourth Zolotarev Problems in the Complex Plane
• A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations
• Low Rank Solution of Lyapunov Equations
• Two Purposes for Matrix Factorization: A Historical Appraisal
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• Matrix Equation $XA + BX = C$
• ZOLOTAREV PROBLEMS CONNECTED WITH RATIONAL FUNCTIONS
• Extended Application of Alternating Direction Implicit Iteration Model Problem Theory
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