Super-fast validated solution of linear systems

DOI10.1016/j.cam.2005.07.038zbMath1108.65020OpenAlexW1974511919MaRDI QIDQ861871

Takeshi Ogita, Siegfried Michael Rump

Publication date: 2 February 2007

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.2005.07.038

zbMATH Keywords

numerical resultsinterval arithmeticself-validating methodssparse linear systemsINTLABCholesky decompositionsymmetric positive definite matrixverified error boundssuper-fast validation algorithm

Mathematics Subject Classification ID

Interval and finite arithmetic (65G30) Direct numerical methods for linear systems and matrix inversion (65F05) Algorithms with automatic result verification (65G20)

Related Items (7)

Interval arithmetic for nonlinear problem solving ⋮ Solving systems of linear fuzzy equations by parametric functions -- an improved algorithm ⋮ Fast verified solutions of linear systems ⋮ On verified numerical computations in convex programming ⋮ Correct approximation of IEEE 754 floating-point arithmetic for program verification ⋮ Rigorous verification of feasibility ⋮ Shifted Cholesky QR for Computing the QR Factorization of Ill-Conditioned Matrices

Uses Software

• BLAS
• INTLAB
• mctoolbox
• Harwell-Boeing sparse matrix collection
• XBLAS

Cites Work

• Fast verification of solutions of matrix equations
• Computation of sharp rigorous componentwise error bounds for the approximate solutions of systems of linear equations
• Interval Methods for Systems of Equations
• Accuracy and Stability of Numerical Algorithms
• Design, implementation and testing of extended and mixed precision BLAS
• Accurate Sum and Dot Product
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