The Schur aggregation and solving ill conditioned linear systems: the convergence theorem

DOI10.1007/s13370-012-0066-xzbMath1276.65018OpenAlexW2071151591MaRDI QIDQ384796

Abdramane Sermé, Jean W. Richard

Publication date: 28 November 2013

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

Full work available at URL: https://doi.org/10.1007/s13370-012-0066-x

zbMATH Keywords

singular value decompositionpreconditioningill conditioned linear systemiterative refinement or improvementSchur aggregationSMW formula

Mathematics Subject Classification ID

Numerical computation of matrix norms, conditioning, scaling (65F35) Direct numerical methods for linear systems and matrix inversion (65F05) Linear equations (linear algebraic aspects) (15A06)

Related Items

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

Uses Software

• Matlab

Cites Work

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• 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
• Accurate Floating-Point Summation Part I: Faithful Rounding
• Accurate Sum and Dot Product
• Certification of numerical computation of the sign of the determinant of a matrix

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