Accurate solution of dense linear systems. II: Algorithms using directed rounding

DOI10.1016/j.cam.2012.09.024zbMath1260.65034OpenAlexW2024194142MaRDI QIDQ1932771

Siegfried Michael Rump

Publication date: 21 January 2013

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2012.09.024

zbMATH Keywords

linear systemsill-conditioned linear systemsrigorous error bounds(extremely) ill-conditioned matricesdata with tolerancesinner bounds

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22) Direct numerical methods for linear systems and matrix inversion (65F05) Algorithms with automatic result verification (65G20)

Related Items (8)

Correct approximation of IEEE 754 floating-point arithmetic for program verification ⋮ Verified numerical computations for large-scale linear systems. ⋮ A method for verifying the accuracy of numerical solutions of symmetric saddle point linear systems ⋮ Verified eigenvalue and eigenvector computations using complex moments and the Rayleigh-Ritz procedure for generalized Hermitian eigenvalue problems ⋮ Unnamed Item ⋮ Computing Enclosures for the Matrix Exponential ⋮ Enclosing Chebyshev Expansions in Linear Time ⋮ Modified error bounds for approximate solutions of dense linear systems

Uses Software

• INTLIB
• Matlab
• PROFIL/BIAS
• INTLAB
• b4m
• VERSOFT

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