Stable modification of explicitLU factors for simplex updates

DOI10.1007/BF02591933zbMath0574.65057OpenAlexW1973589970MaRDI QIDQ3692731

S. P. J. Matthews, Roger Fletcher

Publication date: 1984

Published in: Mathematical Programming (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02591933

zbMATH Keywords

error analysisnumerical stabilityLU factorizationsimplex methodill-conditioned problemsNumerical resultspivotal strategiesexplicit modificationsimplex update

Mathematics Subject Classification ID

Factorization of matrices (15A23) Numerical mathematical programming methods (65K05) Linear programming (90C05) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (10)

A pivoting algorithm for linear programming with linear complementarity constraints ⋮ On error growth in the Bartels-Golub and Fletcher-Matthews algorithms for updating matrix factorizations ⋮ Degeneracy in the presence of roundoff errors ⋮ A splitting-free vorticity redistribution method ⋮ Stable algorithm for updating denseLUfactorization after row or column exchange and row and column addition or deletion ⋮ Unnamed Item ⋮ qpOASES: a parametric active-set algorithm for~quadratic programming ⋮ On the use of dense matrix techniques within sparse simplex ⋮ Sensitivity method for basis inverse representation in multistage stochastic linear programming problems ⋮ A reduced proximal-point homotopy method for large-scale non-convex BQP

Cites Work

• Triangular factors of modified matrices
• A stabilization of the simplex method
• A numerically stable form of the simplex algorithm
• The Elimination form of the Inverse and its Application to Linear Programming
• A Stable Algorithm for Updating Triangular Factors Under a Rank One Change
• Large-scale linear programming: Geometry, working bases and factorizations
• Updated triangular factors of the basis to maintain sparsity in the product form simplex method
• The simplex method of linear programming using LU decomposition
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