On numerical stability in large scale linear algebraic computations

DOI10.1002/zamm.200410185zbMath1069.65030OpenAlexW2141853965MaRDI QIDQ4680363

Zdeněk Strakoš, Jörg Liesen

Publication date: 1 June 2005

Published in: ZAMM (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/zamm.200410185

zbMATH Keywords

algorithmsconvergencenumerical examplesLanczos methodaccuracyerror boundsconjugate gradient methoditerative methodsnumerical stabilityeigenvalue problemsGMRES methodrounding errorslinear algebraic systemsbackward errorbackward stabilitygeneralised minimal residual method

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Iterative numerical methods for linear systems (65F10) Roundoff error (65G50) Algorithms with automatic result verification (65G20)

Related Items

Distribution of the discretization and algebraic error in numerical solution of partial differential equations ⋮ Inexact Half-Quadratic Optimization for Linear Inverse Problems ⋮ Interplay between discretization and algebraic computation in adaptive numerical solutionof elliptic PDE problems

Uses Software

• LSQR
• mctoolbox

Cites Work

• Private Observation, Communication and Collusion
• An Iterative Least-Square Method Suitable for Solving Large Sparse Matrices
• On the Compatibility of a Given Solution With the Data of a Linear System
• Methods of conjugate gradients for solving linear systems
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