A Collection of Problems for Which Gaussian Elimination with Partial Pivoting is Unstable

DOI10.1137/0914013zbMath0771.65049OpenAlexW1999202513MaRDI QIDQ5286344

Stephen J. Wright

Publication date: 29 June 1993

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/e8bcc738629dde68ae294424d46de2d1116c0320

zbMATH Keywords

linear systemsGaussian eliminationnumerical instabilitytwo-point boundary value problemspartial pivoting

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Linear boundary value problems for ordinary differential equations (34B05) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (14)

Floating-point arithmetic on the test bench. How are verified numerical solutions calculated? ⋮ Convergence and instability in PCG methods for bordered systems ⋮ Growth factor and expected growth factor of some pivoting strategies ⋮ The growth factor and efficiency of Gaussian elimination with rook pivoting ⋮ Cyclic reduction, dichotomy, and the estimation of differential equations ⋮ Hadamard Matrices: Insights into Their Growth Factor and Determinant Computations ⋮ A massively parallel algorithm for bordered almost block diagonal systems on GPUs ⋮ Random Matrices Generating Large Growth in LU Factorization with Pivoting ⋮ Computing periodic deflating subspaces associated with a specified set of eigenvalues ⋮ Improved componentwise verified error bounds for least squares problems and underdetermined linear systems ⋮ Linear system solvers for boundary value ODEs ⋮ A collection of examples where Neville elimination outperforms Gaussian elimination ⋮ Almost block diagonal linear systems: sequential and parallel solution techniques, and applications ⋮ Probabilistic analysis of complex Gaussian elimination without pivoting

This page was built for publication: A Collection of Problems for Which Gaussian Elimination with Partial Pivoting is Unstable