Accurate solution of dense linear systems I: Algorithms in rounding to nearest

DOI10.1016/j.cam.2012.10.010zbMath1255.65084OpenAlexW2071442336MaRDI QIDQ1932770

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.2012.10.010

zbMATH Keywords

linear systemerror analysiserror-free transformationrigorous error bounds(extremely) ill-conditionedrounding to nearest

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22)

Related Items (6)

Floating-point arithmetic on the test bench. How are verified numerical solutions calculated? ⋮ Verified numerical computations for large-scale linear systems. ⋮ Verified eigenvalue and eigenvector computations using complex moments and the Rayleigh-Ritz procedure for generalized Hermitian eigenvalue problems ⋮ On the iterative refinement of the solution of ill-conditioned linear system of equations ⋮ Verified partial eigenvalue computations using contour integrals for Hermitian generalized eigenproblems ⋮ A fast and efficient algorithm for solving ill-conditioned linear systems

Uses Software

• Matlab
• BLAS
• MPFR
• INTLAB
• ARPREC
• XBLAS

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