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Reinversion with the preassigned pivot procedure
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Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1137/1004088openalex-snapshot
On an Approach to Techniques for the Analysis of the Structure of Large Systems of Equations
inferredcites →https://doi.org/10.1287/mnsc.3.3.255openalex-snapshot
The Elimination form of the Inverse and its Application to Linear Programming
inferredcites →https://doi.org/10.2307/2283027openalex-snapshot
Recent Advances in Mathematical Programming.
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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A sparse computation system for process design and simulation: Part I. Data structures and processing techniques
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Geometry of the Feasible Region
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Dynamic factorization in large-scale optimization
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Solving staircase linear programs by the simplex method, 1: Inversion
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Identification of special structure constraints in linear programs
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Updated triangular factors of the basis to maintain sparsity in the product form simplex method
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A sparsity-exploiting variant of the Bartels—Golub decomposition for linear programming bases
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Determining GUB sets via an invert agenda algorithm
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Large-scale linearly constrained optimization
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Advanced basis construction in linear programming
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Modifying the forrest-Tomlin and saunders updates for linear programming problems with variable upper bounds
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Network reoptimization procedures for multiobjective network probelems
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Nonlinear multicommodity network flows through primal partitioning and comparison with alternative methods
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Numerical implementation and computational results of nonlinear network optimization with linear side constraints
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A manifold-based approach to sparse global constraint satisfaction problems
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A robust approach for finding all well-separated solutions of sparse systems of nonlinear equations
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Sparse matrix methods for equation-based chemical process flowsheeting—I
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A pathological case in the reduction of linear programs
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Procédures d'optimisation de cascades de réacteurs avec ou sans recyclage
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Integration of nonconvexities/nonlinearities in wastewater treatment engineering design into production cost functions for ethylene
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Packed data structure and supersparsity savings in a linear programming code
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Reoptimization procedures for networks with side constraints
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A parallel processing algorithm for nonlinear programming problems
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Improving the utilization of training resources through optimal personnel assignment in the U.S. Navy
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An implementation of linear and nonlinear multicommodity network flows
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OPTIMIZATION FOR SPARSE SYSTEMS
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A FAST, STABLE IMPLEMENTATION OF THE SIMPLEX METHOD USING BARTELS-GOLUB UPDATING††Research for this paper was supported by the Energy Research and Development Administration Contract AT(04-3)-326 PA #18, at Stanford University.
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IMPLEMENTATION ASPECTS OF MODEL MANAGEMENT: A FOCUS ON COMPUTER-ASSISTED ANALYSIS
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Automatic initial value generation procedure for nonlinear process models by interval arithmetic based cutting and splitting
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An Investigation of Algorithms Used in the Restructuring of Linear Programming Basis Matrices Prior to Inversion
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Recovery from Numerical Instability during Basis Reinversion
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Pricing for sparsity in the revised simplex method
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The Evolution of Mathematical Programming Systems
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Construction of LU Factors of the Basis to Reduce Build-Up during Simplex Iterations
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Multicommodity Network Problems: Applications and Computations
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On a dual method for a specially structured linear programming problem with application to stochastic programming
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Methods for computing and modifying the 𝐿𝐷𝑉 factors of a matrix
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Direct Methods for Sparse Matrices
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Glossary of Symbols
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Copyright Page
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Introduction
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Sparse matrices: storage schemes and simple operations
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Gaussian elimination for dense matrices: the algebraic problem
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Gaussian elimination for dense matrices: numerical considerations
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Gaussian elimination for sparse matrices: an introduction
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Reduction to block triangular form
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Local pivotal strategies for sparse matrices
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Ordering sparse matrices for band solution
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Orderings based on dissection
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Implementing Gaussian elimination without symbolic factorize
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Implementing Gaussian elimination with symbolic factorize
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Gaussian elimination using trees
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Graphs for symmetric and unsymmetric matrices
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The solve phase
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Other sparsity-oriented issues
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Matrix and vector norms
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Pictures of sparse matrices
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Solutions to selected exercises
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Distributed price-directive decomposition applications in power systems operations
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A survey of sparse matrix research
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A survey of third-generation simulation techniques
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On bordered triangular or lower N forms of an irreducible matrix
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The identification of essential variables of systems of algebraic equations applying Gauss- Jordan elimination
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applying a reduced gradient in quadratic programming
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A Structurally Stable Modification of Hellerman–Rarick’s ${\text{P}}^4 $ Algorithm for Reordering Unsymmetric Sparse Matrices
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Sparse Matrix Methods in Optimization
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Direct Methods for Solving Sparse Systems of Linear Equations
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Evaluation of Orderings for Unsymmetric Sparse Matrices
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Use of the ${\text{P}}^4 $ and ${\text{P}}^5 $ Algorithms for In-Core Factorization of Sparse Matrices
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The apex systems past and future
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A Functional Description of ANALYZE: A Computer-Assisted Analysis System for Linear Programming Models
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A Status Report on Computing Algorithms for Mathematical Programming
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Maintaining a Sparse Inverse in the Simplex Method
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Alternative Methods for Representing the Inverse of Linear Programming Basis Matrices
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Implementing an LU Factorization for the Embedded Network Simplex Algorithm
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A Spike Collective Dynamic Factorization Algorithm for the Simplex Method
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Automatic Identification of Generalized Upper Bounds in Large-Scale Optimization Models
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An Application of Mathematical Programming to Assess Productivity in the Houston Independent School District
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A Forward Simplex Method for Staircase Linear Programs
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The Principal Maxmin Matrix Transversal Strategy
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A Decomposition Methodology and a Class of Algorithms for the Solution of Nonlinear Equations
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Technical Note—Dynamic Generalized Upper Bounding
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Technical Note—Computational Comparison among Three Multicommodity Network Flow Algorithms
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Solving Real-World Linear Programs: A Decade and More of Progress
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A review of the LU update in the simplex algorithm
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A Matrix Factorization and Its Application to Large-Scale Linear Programming
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