NUMERICAL SOLUTION OF DISCRETE STABLE LINEAR MATRIX EQUATIONS ON MULTICOMPUTERS

DOI10.1080/10637190208941436zbMath1009.65039OpenAlexW2013268848MaRDI QIDQ3150027

Peter Benner, Gregorio Quintana-Ortí, Enrique S. Quintana-Ortí

Publication date: 6 February 2003

Published in: Parallel Algorithms and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10637190208941436

zbMATH Keywords

performancenumerical examplesparallel computationfilteringimage restorationCayley transformationStein equationssign function methoddiscrete-time control problemssquared Smith iterationdiscrete Sylvester equations

Mathematics Subject Classification ID

Related Items (10)

Partial Stabilization of Descriptor Systems Using Spectral Projectors ⋮ Computational Methods for Linear Matrix Equations ⋮ On the squared Smith method for large-scale Stein equations ⋮ Iterative and doubling algorithms for Riccati‐type matrix equations: A comparative introduction ⋮ Electricity consumption prediction with functional linear regression using spline estimators ⋮ On the numerical solution of large-scale sparse discrete-time Riccati equations ⋮ A structured matrix approach to efficient calculation of LQG repetitive learning controllers in the lifted setting ⋮ Solving stable Sylvester equations via rational iterative schemes ⋮ Numerical algorithms for solving discrete Lyapunov tensor equation ⋮ Fitting Matrix Geometric Distributions by Model Reduction

Uses Software

• LAPACK
• ScaLAPACK
• SLICOT
• mctoolbox

Cites Work

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• A note on Hammarling's algorithm for the discrete Lyapunov equation
• Balancing a matrix for calculation of eigenvalues and eigenvectors
• A Hessenberg-Schur method for the problem AX + XB= C
• Linear model reduction and solution of the algebraic Riccati equation by use of the sign function†
• Numerical Solution of the Stable, Non-negative Definite Lyapunov Equation Lyapunov Equation
• A numerical algorithm to solve<tex>A^{T}XA - X = Q</tex>
• ScaLAPACK Users' Guide
• Solution of the Sylvester matrix equation AXB ^T + CXD ^T = E
• Algorithm 705; a FORTRAN-77 software package for solving the Sylvester matrix equation AXB ^T + CXD ^T = E
• A Parallel Implementation of the Nonsymmetric QR Algorithm for Distributed Memory Architectures
• Application of ADI Iterative Methods to the Restoration of Noisy Images
• Parallelizing the QR Algorithm for the Unsymmetric Algebraic Eigenvalue Problem: Myths and Reality
• Matrix Equation $XA + BX = C$

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