A fast and efficient algorithm for solving ill-conditioned linear systems

DOI10.14495/jsiaml.7.1OpenAlexW2005342300MaRDI QIDQ3121374

Yuka Kobayashi, Takeshi Ogita

Publication date: 18 March 2019

Published in: JSIAM Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.14495/jsiaml.7.1

zbMATH Keywords

floating-point arithmeticaccurate algorithmpreconditioned techniquesolutions of linear systems

Mathematics Subject Classification ID

Fluid mechanics (76-XX) Numerical analysis (65-XX)

Related Items (4)

Balanced incomplete factorization preconditioner with pivoting ⋮ A New Analysis of Iterative Refinement and Its Application to Accurate Solution of Ill-Conditioned Sparse Linear Systems ⋮ On the iterative refinement of the solution of ill-conditioned linear system of equations ⋮ A Maximum-Principle-Preserving Third Order Finite Volume SWENO Scheme on Unstructured Triangular Meshes

Uses Software

• LAPACK
• mctoolbox

Cites Work

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• Inversion of extremely ill-conditioned matrices in floating-point
• Accurate solution of dense linear systems I: Algorithms in rounding to nearest
• Tight and efficient enclosure of matrix multiplication by using optimized BLAS
• Accurate Matrix Factorization: Inverse LU and Inverse QR Factorizations
• Accuracy and Stability of Numerical Algorithms
• Accurate Sum and Dot Product

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