Backward error analysis of the extended iterative refinement or improvement algorithm for solving ill conditioned linear system

DOI10.1007/s13370-013-0216-9zbMath1320.65059OpenAlexW2058198190MaRDI QIDQ2516943

Abdramane Sermé

Publication date: 4 August 2015

Published in: Afrika Matematika (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13370-013-0216-9

zbMATH Keywords

algorithmnumerical examplesingular value decompositionbackward error analysisSherman-Morrison-Woodbury formulaiterative refinement or improvementSchur aggregationSMW formulaadditive preconditioningill-conditioned linear system

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Ill-posedness and regularization problems in numerical linear algebra (65F22) Preconditioners for iterative methods (65F08)

Cites Work

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• The Schur aggregation and solving ill conditioned linear systems: the convergence theorem
• Methods of aggregation
• A probabilistic remark on algebraic program testing
• Additive preconditioning and aggregation in matrix computations
• A floating-point technique for extending the available precision
• The Accuracy of Floating Point Summation
• Error bounds from extra-precise iterative refinement
• Accuracy and Stability of Numerical Algorithms
• Certification of numerical computation of the sign of the determinant of a matrix

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