A collection of examples where Neville elimination outperforms Gaussian elimination

DOI10.1016/j.amc.2010.03.094zbMath1196.65062OpenAlexW2096499832MaRDI QIDQ984263

Pedro Alonso, Rafael Gallego, Jorge Delgado, Juan Manuel Peña

Publication date: 19 July 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2010.03.094

zbMATH Keywords

stabilitynumerical examplesGaussian eliminationtotally positive matricesNeville eliminationiterative refinement

Mathematics Subject Classification ID

Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items

Tests for the recognition of total positivity, A note on matrices with maximal growth factor for Neville elimination, Increasing data locality and introducing level-3 BLAS in the neville elimination, Almost strictly sign regular matrices and Neville elimination with two-determinant pivoting, Structured backward error analysis for sparse polynomial eigenvalue problems

Uses Software

• Matlab
• mctoolbox
• Algorithm 694
• testmatrix

Cites Work

• Backward error analysis of Neville elimination
• Progressive iterative approximation and bases with the fastest convergence rates
• Sign regular matrices and Neville elimination
• Blocking Neville elimination algorithm for exploiting cache memories
• Total positivity and Neville elimination
• Almost strictly totally positive matrices
• Scaled pivoting in Gauss and Neville elimination for totally positive systems
• A matricial description of Neville elimination with applications to total positivity
• A stable test for strict sign regularity
• Iterative refinement for Neville elimination
• Scaling for Numerical Stability in Gaussian Elimination
• Iterative Refinement Implies Numerical Stability for Gaussian Elimination
• Gaussian Elimination with Partial Pivoting Can Fail in Practice
• Algorithm 694
• A Totally Positive Factorization of Rectangular Matrices by the Neville Elimination
• Large Growth Factors in Gaussian Elimination with Pivoting
• A Collection of Problems for Which Gaussian Elimination with Partial Pivoting is Unstable
• The Accurate and Efficient Solution of a Totally Positive Generalized Vandermonde Linear System
• Iterative Refinement in Floating Point
• Totally positive matrices
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