Computationally enhanced projection methods for symmetric Sylvester and Lyapunov matrix equations

DOI10.1016/j.cam.2017.08.011zbMath1503.65087arXiv1602.05033OpenAlexW2962856060MaRDI QIDQ1675996

Valeria Simoncini, Davide Palitta

Publication date: 3 November 2017

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.05033

zbMATH Keywords

Lyapunov equationprojection methodsSylvester equationKrylov subspaces

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Numerical methods for matrix equations (65F45)

Related Items (7)

Solutions to matrix equations \(X - AXB = CY + R\) and \(X - A\hat{X}B = CY + R\) ⋮ Solving Rank-Structured Sylvester and Lyapunov Equations ⋮ Generalized conjugate direction algorithm for solving generalized coupled Sylvester transpose matrix equations over reflexive or anti-reflexive matrices ⋮ State-dependent Riccati equation feedback stabilization for nonlinear PDEs ⋮ A Krylov Subspace Method for the Approximation of Bivariate Matrix Functions ⋮ Optimality properties of Galerkin and Petrov-Galerkin methods for linear matrix equations ⋮ Matrix equation techniques for certain evolutionary partial differential equations

Uses Software

• Algorithm 432

Cites Work

• Unnamed Item
• Low-rank solvers for fractional differential equations
• Matrix-equation-based strategies for convection-diffusion equations
• Adaptive rational Krylov subspaces for large-scale dynamical systems
• Short recurrences for computing extended Krylov bases for Hermitian and unitary matrices
• The extended Krylov subspace method and orthogonal Laurent polynomials
• Eigenvalue decay bounds for solutions of Lyapunov equations: the symmetric case
• Computational Methods for Linear Matrix Equations
• A New Iterative Method for Solving Large-Scale Lyapunov Matrix Equations
• Stopping Criteria for Rational Matrix Functions of Hermitian and Symmetric Matrices
• Numerical Solution of the Stable, Non-negative Definite Lyapunov Equation Lyapunov Equation
• Krylov Subspace Methods for Solving Large Lyapunov Equations
• A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations
• Isogeometric Analysis
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• The Matrix Eigenvalue Problem
• On Nonnegative Solutions of the Equation $AD + DA' = - C$
• Extended Application of Alternating Direction Implicit Iteration Model Problem Theory
• Approximation of Large-Scale Dynamical Systems

This page was built for publication: Computationally enhanced projection methods for symmetric Sylvester and Lyapunov matrix equations