Splitting dense columns in sparse linear systems
type: Item
instance of: scholarly article
title: Splitting dense columns in sparse linear systems
zbMATH Open document ID: 0727.65034
DOI: 10.1016/0024-3795(91)90269-3
published in: Linear Algebra and its Applications
publication date: 1991-01-01T00:00:00Z
review text: Let \(A=[S,D]\) where S and D denote respectively the sparse and dense columns of a matrix A. The author gives an efficient and robust method for solving \(AA^ Tx=b.\) The proposed method avoids the rank-deficiency problem that is common to the present algorithms and also makes an effective use of sparse matrix techniques. Applications to interior-point methods for linear programming and non-symmetric matrices are pointed out.
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 65F50
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 4201484
zbMATH Keywords: splitting dense columns
zbMATH Keywords: sparse matrix
zbMATH Keywords: interior-point methods
zbMATH Keywords: linear programming
zbMATH Keywords: non-symmetric matrices
author: Robert J. Vanderbei
describes a project that uses: ALPO
MaRDI profile type: Publication
full work available at URL: 0024-3795(91)90269-3
OpenAlex ID: W2093058960
cites work: On projected newton barrier methods for linear programming and an equivalence to Karmarkar’s projective method
cites work: An implementation of Karmarkar's algorithm for linear programming
cites work: Data Structures and Programming Techniques for the Implementation of Karmarkar's Algorithm
cites work: Implementations of Affine Scaling Methods: Approximate Solutions of Systems of Linear Equations Using Preconditioned Conjugate Gradient Methods
cites work: Further Development of a Primal-Dual Interior Point Method
cites work: Q4288553
cites work: Computational experience with a primal-dual interior point method for linear programming
cites work: Implementation of a Dual Affine Interior Point Algorithm for Linear Programming
cites work: An Implementation of a Primal-Dual Interior Point Method for Linear Programming
cites work: On Implementing Mehrotra’s Predictor–Corrector Interior-Point Method for Linear Programming
cites work: ALPO: Another Linear Program Optimizer
cites work: Formulating Two-Stage Stochastic Programs for Interior Point Methods
cites work: The Optimal Choice of a Subset of a Population
description: scientific article; zbMATH DE number 4201484