Finite precision behavior of stationary iteration for solving singular systems

DOI10.1016/0024-3795(93)90242-GzbMath0787.65021WikidataQ56998989 ScholiaQ56998989MaRDI QIDQ1311321

Nicholas J. Higham, Philip A. Knight

Publication date: 26 January 1994

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

numerical examplesGauss-Seidel iterationsingular systemsperturbation boundRichardson iterationfinite precision arithmeticstationary iterationforward and backward stability

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10)

Related Items

Numerical stability of GMRES, Properties and characterizations of dual sharp orders, Rounding error analysis of two-stage iterative methods for large linear systems, Perturbation analysis of singular linear systems with arbitrary index., Convergence properties of Krylov subspace methods for singular linear systems with arbitrary index, Expressions for the drazin inverse of a 2×2 Block Matrix, An improvement on the perturbation of the group inverse and oblique projection, The Drazin inverse of updating of a square matrix with application to perturbation formula, Successive matrix squaring algorithm for computing the Drazin inverse, On the perturbation of the group inverse and oblique projection, Perturbation analysis of singular linear systems with index one^∗, The perturbation bounds for the solution of weighted Kronecker product linear systems using the \(W\)-weighted Drazin inverse

Cites Work

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• Round-off error analysis of iterations for large linear systems
• Numerical stability of the cyclic Richardson iteration
• Regular splittings and the discrete Neumann problem
• Matrix Methods for Queuing Problems
• Matrix Analysis
• Convergent Powers of a Matrix with Applications to Iterative Methods for Singular Linear Systems
• On the Solution of Singular and Semidefinite Linear Systems by Iteration
• The Convergence of Linear Stationary Iterative Processes for Solving Singular Unstructured Systems of Linear Equations