Some Results on Sparse Matrices

DOI10.2307/2004627zbMath0233.65022OpenAlexW4237657905MaRDI QIDQ5641963

Ralph A. Willoughby, Fred G. Gustavson, Robert K. Brayton

Publication date: 1971

Full work available at URL: https://doi.org/10.2307/2004627

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items

A survey of the advances in the exploitation of the sparsity in the solution of large problems, Degree switching operations in networks and large scale systems assignment problems, On the efficient computation of the nonlinear full-information maximum- likelihood estimator, The efficient solution of large-scale linear programming problems—some algorithmic techniques and computational results, On solving problems with sparse matrices, On the Number of Nonzeros Added when Gaussian Elimination is Performed on Sparse Random Matrices, Predicting the structure of sparse orthogonal factors, Updated triangular factors of the basis to maintain sparsity in the product form simplex method

Cites Work

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• Optimally scaled matrices
• A graph theoretic approach to matrix inversion by partitioning
• Solution of real and complex systems of linear equations
• The Elimination form of the Inverse and its Application to Linear Programming
• Evolution of Linear Programming Computing Techniques
• A Survey of Some Closed Methods for Inverting Matrices
• Algorithms for the Assignment and Transportation Problems
• Solution of Certain Large Sets of Equations on Pegasus using Matrix Methods
• Decomposition Principle for Linear Programs
• A Note on Systems of Linear Equations
• The Use of Linear Graphs in Gauss Elimination
• The Decomposition Algorithm for Linear Programs
• On Pre-Conditioning of Matrices
• The Analysis of Large Structural Systems
• An Algorithm for Scaling Matrices
• Error Analysis of Direct Methods of Matrix Inversion
• The Inversion of Matrices by Flow Graphs
• A Compact Storage Scheme for the Solution of Symmetric Linear Simultaneous Equations
• Graphs and Matrices
• An algorithm for reducing the bandwidth of a matrix of symmetrical configuration
• Admissible Solutions of Linear Systems with Not Sharply Defined Coefficients
• Computable Error Bounds for Direct Solution of Linear Equations
• The Inversion of Sparse Matrices by a Strategy Derived from their Graphs
• Row-column permutation of sparse matrices
• Solution of linear equations with coefficient matrix in band form
• Minimization of the number of arithmetic operations in the solution of linear algebraic systems of equations
• Optimal elimination for sparse symmetric systems as a graph problem.
• An empirical estimate of the relative error of the computed solution x of Ax = b
• The Decomposition of Economic Production Systems
• The Product Form of Inverses of Sparse Matrices and Graph Theory
• Solving linear least squares problems by Gram-Schmidt orthogonalization
• Symbolic Generation of an Optimal Crout Algorithm for Sparse Systems of Linear Equations
• On the number of multiplications necessary to compute certain functions
• A Graph Technique for Inverting Certain Matrices
• On the Product Form of Inverses of Sparse Matrices
• Solution of a system of simultaneous linear equations with a sparse coefficient matrix by elimination methods
• Numerical Linear Algebra
• On the Inversion of Sparse Matrices
• Two Algorithms for Bipartite Graphs
• ROUNDING-OFF ERRORS IN MATRIX PROCESSES
• The Product Form for the Inverse in the Simplex Method
• On Best Conditioned Matrices