BACKWARD PERTURBATION ANALYSIS AND RELATIVE ALGORITHMS FOR NONSYMMETRIC LINEAR SYSTEMS WITH MULTIPLE RIGHT-HAND SIDES

DOI10.17654/NT039060959OpenAlexW2780754448MaRDI QIDQ5075073

Xi-Lan Liu, Zhanshan Yang

Publication date: 10 May 2022

Published in: JP Journal of Algebra, Number Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.17654/nt039060959

zbMATH Keywords

iterative methodsKronecker productbackward perturbationblock methodsmultiple right-hand sidesnonsymmetric linear systemsmatrix Krylov subspaceglobal Arnoldiminimum joint backward perturbation

Mathematics Subject Classification ID

Numerical linear algebra (65Fxx)

Uses Software

• GMBACK
• VanHuffel

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An Analysis of the Total Least Squares Problem
• Algebraic connections between the least squares and total least squares problems
• The block conjugate gradient algorithm and related methods
• A new look at the Lanczos algorithm for solving symmetric systems of linear equations
• Eigenvalues and pseudo-eigenvalues of Toeplitz matrices
• Block-Arnoldi and Davidson methods for unsymmetric large eigenvalue problems
• Iterative solution of multiple radiation and scattering problems in structural acoustics using a block quasi-minimal residual algorithm
• Global FOM and GMRES algorithms for matrix equations
• Perturbation analysis of the maximal solution of the matrix equation \(X+A^*X^{-1}A=P\). II
• Convergence properties of block GMRES and matrix polynomials
• Analysis of a Minimum Perturbation Algorithm for Nonsymmetric Linear Systems
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• The computation of Lagrange-multiplier estimates for constrained minimization
• Krylov Subspace Methods for Solving Large Unsymmetric Linear Systems
• A Hybrid GMRES Algorithm for Nonsymmetric Linear Systems
• Kronecker products and matrix calculus in system theory
• Analysis of Projection Methods for Solving Linear Systems with Multiple Right-Hand Sides
• Schur complements and matrix inequalities of hadamard products^∗
• On the Lanczos Method for Solving Symmetric Linear Systems with Several Right-Hand Sides
• GMBACK: A Generalised Minimum Backward Error Algorithm for Nonsymmetric Linear Systems
• An Iterative Method for Nonsymmetric Systems with Multiple Right-Hand Sides
• Variable Block CG Algorithms for Solving Large Sparse Symmetric Positive Definite Linear Systems on Parallel Computers, I: General Iterative Scheme
• Trace and Eigenvalue Inequalities for Ordinary and Hadamard Products of Positive Semidefinite Hermitian Matrices
• Explicit Solutions of Linear Matrix Equations
• A Theoretical Comparison of the Arnoldi and GMRES Algorithms
• The principle of minimized iterations in the solution of the matrix eigenvalue problem

This page was built for publication: BACKWARD PERTURBATION ANALYSIS AND RELATIVE ALGORITHMS FOR NONSYMMETRIC LINEAR SYSTEMS WITH MULTIPLE RIGHT-HAND SIDES