Gaussian Elimination with Partial Pivoting Can Fail in Practice

DOI10.1137/S0895479892239755zbMath0806.65022OpenAlexW1976662650MaRDI QIDQ4313383

Leslie V. Foster

Publication date: 16 November 1994

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0895479892239755

zbMATH Keywords

numerical stabilityVolterra integral equations of the second kindfirst-order differential equationerror growthGaussian elimination with partial pivoting

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Roundoff error (65G50) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (7)

Floating-point arithmetic on the test bench. How are verified numerical solutions calculated? ⋮ Growth factor and expected growth factor of some pivoting strategies ⋮ The growth factor and efficiency of Gaussian elimination with rook pivoting ⋮ Hadamard Matrices: Insights into Their Growth Factor and Determinant Computations ⋮ Random Matrices Generating Large Growth in LU Factorization with Pivoting ⋮ A collection of examples where Neville elimination outperforms Gaussian elimination ⋮ Probabilistic analysis of complex Gaussian elimination without pivoting

Uses Software

• Regularization tools
• Harwell-Boeing sparse matrix collection
• Algorithm 694

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