A survey of sparse matrix research

Graph theory

1969 • 11,244 citations

The Hungarian method for the assignment problem

1955 • 11,128 citations

A Formal Basis for the Heuristic Determination of Minimum Cost Paths

1968 • 10,580 citations

The Design and Analysis of Computer Algorithms

1974 • 9,688 citations

Methods of conjugate gradients for solving linear systems

1952 • 7,639 citations

Linear Programming and Extensions

1963 • 5,853 citations

Matrix Iterative Analysis

2000 • 5,826 citations

Depth-First Search and Linear Graph Algorithms

1972 • 5,699 citations

The Algebraic Eigenvalue Problem

1966 • 5,231 citations

The finite element method in engineering science

1971 • 4,380 citations

An iteration method for the solution of the eigenvalue problem of linear differential and integral operators

1950 • 4,159 citations

Matrix Iterative Analysis

1963 • 4,155 citations

Algorithms for the Assignment and Transportation Problems

1957 • 3,764 citations

Numerical Initial Value Problems in Ordinary Differential Equations

1972 • 3,569 citations

An Analysis of the Finite Element Method

1974 • 3,452 citations

The Numerical Solution of Parabolic and Elliptic Differential Equations

1955 • 3,182 citations

An $n^{5/2} $ Algorithm for Maximum Matchings in Bipartite Graphs

1973 • 2,802 citations

Gaussian elimination is not optimal

1969 • 2,455 citations

Introduction to matrix computations

1973 • 2,448 citations

On Representatives of Subsets

1935 • 2,017 citations

Calculating the Singular Values and Pseudo-Inverse of a Matrix

1965 • 1,749 citations

Iterative Solution of Large Linear Systems

1971 • 1,746 citations

Iterative Solution of Implicit Approximations of Multidimensional Partial Differential Equations

1968 • 1,692 citations

A Theorem on Boolean Matrices

1962 • 1,653 citations

A study of replacement algorithms for a virtual-storage computer

1966 • 1,628 citations

Solution of Sparse Indefinite Systems of Linear Equations

1975 • 1,568 citations

Reducing the bandwidth of sparse symmetric matrices

1969 • 1,438 citations

Rounding errors in algebraic processes

1964 • 1,377 citations

Methods in Computational Physics

1971 • 1,354 citations

Incidence matrices and interval graphs

1965 • 1,286 citations

THE THEORY OF MATRICES IN NUMERICAL ANALYSIS

1965 • 1,179 citations

Power Flow Solution by Newton's Method

1967 • 1,174 citations

Nested Dissection of a Regular Finite Element Mesh

1973 • 1,017 citations

Linear Programming and Extensions.

1964 • 1,008 citations

A Programming Language

1962 • 920 citations

A frontal solution program for finite element analysis

1970 • 901 citations

Numerical methods for solving linear least squares problems

1965 • 840 citations

The art of computer programming. Vol.1: Fundamental algorithms

1978 • 828 citations

Direct solutions of sparse network equations by optimally ordered triangular factorization

1967 • 806 citations

Convex structures and economic theory

1968 • 772 citations

On Direct Methods for Solving Poisson’s Equations

1970 • 733 citations

An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix

1977 • 727 citations

The Transitive Reduction of a Directed Graph

1972 • 717 citations

An empirical study of FORTRAN programs

1971 • 688 citations

A Fast Direct Solution of Poisson's Equation Using Fourier Analysis

1965 • 684 citations

Iterative methods for solving partial difference equations of elliptic type

1954 • 663 citations

The QR Transformation A Unitary Analogue to the LR Transformation--Part 1

1961 • 657 citations

The potential calculation and some applications

1970 • 648 citations

Simultaneous Numerical Solution of Differential-Algebraic Equations

1971 • 642 citations

Graph theory and theoretical physics

1967 • 623 citations

Convex structures and economic theory

1968 • 613 citations

Virtual memory

1996 • 586 citations

Unitary Triangularization of a Nonsymmetric Matrix

1958 • 586 citations

An Algorithm for Reducing the Bandwidth and Profile of a Sparse Matrix

1976 • 581 citations

Theorie der endlichen und unendlichen Graphen

1937 • 562 citations

Handbook for Automatic Computation

1971 • 535 citations

The Elimination form of the Inverse and its Application to Linear Programming

1957 • 513 citations

Triangulated graphs and the elimination process

1970 • 496 citations

Least Squares Computations by Givens Transformations Without Square Roots

1973 • 483 citations

Principles of Numerical Analysis

1954 • 474 citations

Solving linear least squares problems by Gram-Schmidt orthogonalization

1967 • 453 citations

Rounding Errors in Algebraic Processes

1964 • 450 citations

Coverings of Bipartite Graphs

1958 • 444 citations

A GENERALIZED CONJUGATE GRADIENT METHOD FOR THE NUMERICAL SOLUTION OF ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS

1976 • 441 citations

A GRAPH-THEORETIC STUDY OF THE NUMERICAL SOLUTION OF SPARSE POSITIVE DEFINITE SYSTEMS OF LINEAR EQUATIONS

1972 • 434 citations

Direct Methods for Solving Symmetric Indefinite Systems of Linear Equations

1971 • 427 citations

Energy Theorems and Structural Analysis

1960 • 411 citations

On the Estimation of Sparse Jacobian Matrices

1974 • 410 citations

Computational Variants of the Lanczos Method for the Eigenproblem

1972 • 403 citations

Numerical and Computer Methods in Structural Mechanics

1973 • 396 citations

Direct methods for sparse matrices

1990 • 394 citations

Virtual Memory

1970 • 389 citations

Handbook for Automatic Computation

1967 • 388 citations

Sparse Matrix Computations

1976 • 386 citations

Variants of the hungarian method for assignment problems

1956 • 376 citations

The finite element method in solid mechanics

2014 • 374 citations

A programming language

1962 • 373 citations

The QR Transformation--Part 2

1962 • 360 citations

Some stable methods for calculating inertia and solving symmetric linear systems

1977 • 356 citations

The Sparse Tableau Approach to Network Analysis and Design

1971 • 341 citations

Triangular factorization and inversion by fast matrix multiplication

1974 • 337 citations

The Direct Solution of the Discrete Poisson Equation on Irregular Regions

1971 • 309 citations

A relaxation method for solving elliptic difference equations

1962 • 301 citations

An O (N2.5) algorithm for maximum matching in general graphs

1975 • 297 citations

The Use of Linear Graphs in Gauss Elimination

1961 • 282 citations

A Simple Algorithm for Finding Maximal Network Flows and an Application to the Hitchcock Problem

1957 • 280 citations

Comparative Analysis of the Cuthill–McKee and the Reverse Cuthill–McKee Ordering Algorithms for Sparse Matrices

1976 • 277 citations

The automatic integration of stiff ordinary differential equations.

1968 • 266 citations

Sparse Matrices and their Applications

1972 • 261 citations

A LISP garbage-collector for virtual-memory computer systems

1969 • 250 citations

The least squares problem and pseudo-inverses

1970 • 249 citations

Computer implementation of the finite element method

1971 • 249 citations

Efficient Integration Methods for Stiff Systems of Ordinary Differential Equations

1970 • 247 citations

Iterative Solution of Elliptic Systems and Applications to the Neutron Diffusion Equations of Reactor Physics

1967 • 229 citations

The Determinant of the Adjacency Matrix of a Graph

1962 • 222 citations

Updated triangular factors of the basis to maintain sparsity in the product form simplex method

1972 • 220 citations

Advanced Linear-Programming Computing Techniques

1968 • 219 citations

The Direct Solution of the Discrete Poisson Equation on a Rectangle

1970 • 217 citations

Introduction to Applied Numerical Analysis.

1971 • 211 citations

On Algorithms for Obtaining a Maximum Transversal

1981 • 207 citations

An Implementation of Tarjan's Algorithm for the Block Triangularization of a Matrix

1978 • 206 citations

Computation of Plain Unitary Rotations Transforming a General Matrix to Triangular Form

1958 • 206 citations

Partitioning and Tearing Systems of Equations

1965 • 205 citations

Modification of a quasi-Newton method for nonlinear equations with a sparse Jacobian

1970 • 197 citations

Computational aspects of F. L. Bauer's simultaneous iteration method

1969 • 197 citations

Advanced Linear-Programming Computing Techniques

1969 • 196 citations

Efficient determination of the transitive closure of a directed graph

1971 • 192 citations

PROCESS ANALYSIS AND SIMULATION

2015 • 191 citations

Decomposition of large-scale problems

1973 • 188 citations

A Generalized Conjugate Gradient Method for Nonsymmetric Systems of Linear Equations

1976 • 187 citations

On an Approach to Techniques for the Analysis of the Structure of Large Systems of Equations

1962 • 184 citations

A Compact Non-Iterative Poisson Solver

1969 • 184 citations

The pfort verifier

1974 • 182 citations

Algorithm for Diagonalization of Large Matrices

1965 • 178 citations

Organizing matrices and matrix operations for paged memory systems

1969 • 178 citations

A sparsity-exploiting variant of the Bartels—Golub decomposition for linear programming bases

1982 • 176 citations

Scatter storage techniques

1968 • 175 citations

Computer Aided Network Design

2006 • 169 citations

Some Aspects of the Cyclic Reduction Algorithm for Block Tridiagonal Linear Systems

1976 • 162 citations

Principles of Numerical Analysis

1955 • 162 citations

FORMATION OF A SPARSE BUS IMPEDANCE MATRIX AND ITS APPLICATION TO SHORT CIRCUIT STUDY

1980 • 160 citations

On the Automatic Scaling of Matrices for Gaussian Elimination

1972 • 159 citations

Topics in Numerical Analysis

1974 • 159 citations

A Compact Storage Scheme for the Solution of Symmetric Linear Simultaneous Equations

1966 • 156 citations

Algorithmic Aspects of Vertex Elimination on Directed Graphs

1978 • 156 citations

A Short Method for Evaluating Determinants and Solving Systems of Linear Equations With Real or Complex Coefficients

1941 • 154 citations

Reinversion with the preassigned pivot procedure

1971 • 154 citations

Flow-Graph Solutions of Linear Algebraic Equations

1959 • 153 citations

Efficient FORTRAN subprograms for the solution of elliptic partial differential equations.

1975 • 149 citations

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1965 • 146 citations

On computing certain elements of the inverse of a sparse matrix

1975 • 144 citations

Symbolic Generation of an Optimal Crout Algorithm for Sparse Systems of Linear Equations

1970 • 141 citations

Simultaneous iteration method for symmetric matrices

1970 • 137 citations

Numerical Methods in Structural Mechanics

1996 • 131 citations

Compensation Methods for Network Solutions by Optimally Ordered Triangular Factorization

1972 • 131 citations

Large Sparse Sets of Linear Equations

1973 • 130 citations

Dynamic space-sharing in computer systems

1969 • 130 citations

Triangular factors of modified matrices

1965 • 129 citations

Computer methods of network analysis

1967 • 128 citations

A Set of Principles to Interconnect the Solutions of Physical Systems

1953 • 128 citations

Some Basic Techniques for Solving Sparse Systems of Linear Equations

1972 • 127 citations

Das Verfahren der Treppeniteration und verwandte Verfahren zur Lösung algebraischer Eigenwertprobleme

1957 • 127 citations

An automatic reordering scheme for simultaneous equations derived from network systems

1970 • 126 citations

A Cyclic Reduction Algorithm for Solving Block Tridiagonal Systems of Arbitrary Dimension

1977 • 125 citations

The Partitioned Preassigned Pivot Procedure (P4)

1972 • 123 citations

Marching Algorithms for Elliptic Boundary Value Problems. I: The Constant Coefficient Case

1977 • 122 citations

Two Algorithms for Bipartite Graphs

1963 • 122 citations

Conjugate gradient methods for partial differential equations.

1978 • 121 citations

A stabilization of the simplex method

1971 • 120 citations

Direct Methods in Reservoir Simulation

1974 • 119 citations

A modification of Warshall's algorithm for the transitive closure of binary relations

1975 • 118 citations

A Note on Modifications to the Givens Plane Rotation

1974 • 118 citations

Techniques for Exploiting the Sparsity or the Network Admittance Matrix

1963 • 118 citations

An algorithm for a minimum cover of a graph

1959 • 117 citations

Solution of linear equations with skyline-stored symmetric matrix

1975 • 116 citations

Sparsity-Directed Decomposition for Gaussian Elimination on Matrices

1970 • 116 citations

Complexity Bounds for Regular Finite Difference and Finite Element Grids

1973 • 116 citations

Complexity of Sequential and Parallel Numerical Algorithms

1973 • 115 citations

Several Strategies for Reducing the Bandwidth of Matrices

1972 • 114 citations

Bidiagonalization of Matrices and Solution of Linear Equations

1974 • 113 citations

Key-to-address transform techniques

1971 • 113 citations

Structured Systems Analysis

2020 • 113 citations

A transitive closure algorithm

1970 • 112 citations

New iterative methods for solution of the eigenproblem

1966 • 108 citations

Note on the iterative refinement of least squares solution

1966 • 108 citations

Tridiagonalization of a symetric band matrix

1968 • 105 citations

Iterative refinement of linear least squares solutions II

1968 • 105 citations

Methods for Modifying Matrix Factorizations

1974 • 105 citations

A method of gradients for the calculation of the characteristic roots and vectors of a real symmetric matrix

1951 • 104 citations

The convergence of an algorithm for solving sparse nonlinear systems

1971 • 104 citations

Stability Analysis of Interconnected Systems

1974 • 103 citations

A graph theoretic approach to matrix inversion by partitioning

1962 • 102 citations

A block Lanczos algorithm for computing the q algebraically largest eigenvalues and a corresponding eigenspace of large, sparse, real symmetric matrices

1974 • 99 citations

The Direct Solution of the Biharmonic Equation on Rectangular Regions and the Poisson Equation on Irregular Regions

1974 • 99 citations

An Introduction to the Analysis of Algorithms

2012 • 98 citations

A sparse matrix method for analysis of piecewise-linear resistive networks

1972 • 97 citations

A numerically stable form of the simplex algorithm

1973 • 97 citations

On the graphs and asymptotic forms of finite boolean relation matrices and stochastic matrices

1957 • 97 citations

A Generalized Cyclic Reduction Algorithm

1974 • 96 citations

A Comparison of Some Methods for the Solution of Sparse Overdetermined Systems of Linear Equations

1976 • 95 citations

A Graph Theoretic Method for the Complete Reduction of a Matrix with a View Toward Finding its Eigenvalues

1959 • 94 citations

NOTES ON THE SOLUTION OF ALGEBRAIC LINEAR SIMULTANEOUS EQUATIONS

1948 • 92 citations

An Algorithm for Distinct Representatives

1956 • 92 citations

On the reduction of a symmetric matrix to tridiagonal form

1971 • 91 citations

The evaluation of eigenvalues and eigenvectors of real symmetric matrices by simultaneous iteration

1970 • 88 citations

Reduction of the symmetric eigenproblemAx=λBx and related problems to standard form

1968 • 88 citations

On Block Elimination for Sparse Linear Systems

1974 • 87 citations

An Optimal Ordering of Electronic Circuit Equations for a Sparse Matrix Solution

1971 • 87 citations

Iterative refinement of linear least squares solutions I

1967 • 84 citations

Symmetric decomposition of positive definite band matrices

1965 • 83 citations

2$sup 1$,$sup 3$P, 3$sup 1$,$sup 3$P, AND 4$sup 1$,$sup 3$ STATES OF He AND THE 2$sup 1$P STATE OF Li$sup +$

1965 • 82 citations

Partial Pivoting Strategies for Symmetric Matrices

1974 • 81 citations

Primal partition programming for block diagonal matrices

1964 • 79 citations

The Solution of Large Sparse Unsymmetric Systems of Linear Equations

1971 • 79 citations

Algorithmic aspects of vertex elimination

1975 • 79 citations

A Survey of Indexing Techniques for Sparse Matrices

1973 • 78 citations

Elimination Methods for Load-Flow Studies

1961 • 78 citations

An Algorithm for Scaling Matrices

1962 • 78 citations

The Use of Conjugate Gradients for Systems of Linear Equations Possessing “Property A”

1972 • 78 citations

Direct solution of large systems of linear equations

1974 • 77 citations

A Survey of Some Closed Methods for Inverting Matrices

1957 • 76 citations

On George’s Nested Dissection Method

1976 • 76 citations

Matrix bandwidth minimization

1968 • 76 citations

An iterative block lanczos method for the solution of large sparse symmetric eigenproblems.

1975 • 75 citations

Methods for computing and modifying the 𝐿𝐷𝑉 factors of a matrix

1975 • 75 citations

Matrix methods in urban and regional analysis

1971 • 73 citations

An iterative method for finding characteristic vectors of a symmetric matrix

1951 • 72 citations

A New Method of Checking the Consistency of Precedence Matrices

1959 • 72 citations

A Method of Block Iteration

1956 • 72 citations

Solution of symmetric and unsymmetric band equations and the calculation of eigenvectors of band matrices

1967 • 70 citations

Application of the simultaneous iteration method to undamped vibration problems

1971 • 70 citations

A Decomposition Algorithm for Shortest Paths in a Network

1968 • 69 citations

Decomposition Procedures for the Solving of Large Scale Systems

1970 • 69 citations

Simultaneous Iteration for Partial Eigensolution of Real Matrices

1975 • 69 citations

Some Generalizations of the Problem of Distinct Representatives

1958 • 68 citations

An Algorithm for Finding a Minimal Equivalent Graph of a Digraph

1975 • 68 citations

A Note on the Stability of Gaussian Elimination

1971 • 67 citations

Analysis of the Diagonal Pivoting Method

1971 • 67 citations

Matrix computations with Fortran and paging

1972 • 66 citations

On the Complexity of Sparse Elimination

1996 • 65 citations

GRAPH THEORY AND GAUSSIAN ELIMINATION

1976 • 65 citations

On computing the transitive closure of a relation

1977 • 65 citations

Some results on sparse matrices

1970 • 64 citations

A Comparison of Sparsity Orderings for Obtaining a Pivotal Sequence in Gaussian Elimination

1974 • 64 citations

On the efficient solution of sparse systems of linear and nonlinear equations.

1975 • 61 citations

Triangular Factorization and Inversion by Fast Matrix Multiplication

1974 • 61 citations

Structuring design computations

1969 • 60 citations

Programming Technique: An improved hash code for scatter storage

1968 • 59 citations

Accelerating the orthogonal iteration for the eigenvectors of a Hermitian matrix

1969 • 58 citations

Self-Avoiding Paths and the Adjacency Matrix of a Graph

1966 • 58 citations

Efficient Solution of Load-Deflection Equations

1969 • 58 citations

An automatic node-relabeling scheme for bandwidth minimization of stiffness matrices.

1968 • 57 citations

On applying Householder transformations to linear least squares problems.

1968 • 57 citations

METHODS FOR SPARSE LINEAR LEAST SQUARES PROBLEMS

1976 • 57 citations

On Permutations to Block Triangular Form

1977 • 57 citations

The Altran system for rational function manipulation — a survey

1971 • 56 citations

Finite Difference Methods for Partial Differential Equations

2012 • 56 citations

Partitioning, tearing and modification of sparse linear systems

1974 • 56 citations

Quasi-tridiagonal matrices and type-insensitive difference equations

1960 • 55 citations

Revised Matrix Algorithms for Shortest Paths

1967 • 55 citations

Solution of large unsymmetric systems of linear equations

1992 • 54 citations

An improved hash code for scatter storage

1983 • 53 citations

An algorithm for reducing the bandwidth of a matrix of symmetrical configuration

1965 • 52 citations

Monitoring the stability of the triangular factorization of a sparse matrix

1974 • 50 citations

Methods of Simultaneous Iteration for Calculating Eigenvectors of Matrices

1975 • 49 citations

Solution of large sparse systems by ordered triangular factorization

1973 • 49 citations

Design variable selection to simplify process calculations

1966 • 48 citations

Decomposition of nets

1972 • 47 citations

On the use of Fast Methods for Separable Finite Difference Equations for the Solution of General Elliptic Problems

1972 • 47 citations

Variational buildup of nuclear shell model bases

1969 • 47 citations

Condition, equilibration and pivoting in linear algebraic systems

1970 • 47 citations

A Simultaneous Iteration Method for the Unsymmetric Eigenvalue Problem

1971 • 46 citations

Solution of eigenvalue problems by sturm sequence method

1972 • 46 citations

On the Bartels—Golub decomposition for linear programming bases

1977 • 46 citations

Minimizing the bandwidth of sparse symmetric matrices

1973 • 46 citations

Hypermatrix solution of large sets of symmetric positive-definite linear equations

1972 • 44 citations

Optimal gradient minimization scheme for finite element eigenproblems

1972 • 43 citations

A note on minimal essential sets

1971 • 40 citations

An equation solver of very large capacity

1971 • 40 citations

An $O(n^2 )$ Method for Solving Constant Coefficient Boundary Value Problems in Two Dimensions

1975 • 39 citations

Sorting in a paging environment

1970 • 39 citations

Methods for Computing and Modifying the LDV Factors of a Matrix

1975 • 39 citations

Solutions of Ax = gamma Bx1

1951 • 38 citations

A direct iteration method of obtaining latent roots and vectors of a symmetric matrix

1967 • 38 citations

Decomposition of large scale systems—I. Systems composed of lumped parameter elements

1966 • 37 citations

Pivot selection and row ordering in givens reduction on sparse matrices

1974 • 36 citations

The eigenvalue problem for symmetric matrices of high order

1974 • 36 citations

The bordered triangular matrix and minimum essential sets of a digraph

1974 • 35 citations

The method of conjugate gradients used in inverse iteration

1972 • 35 citations

Pivoting for Size and Sparsity in Linear Programming Inversion Routes

1972 • 35 citations

The structuring of process optimization

1970 • 35 citations

An Improved Method for Reducing the Bandwidth of Sparse Symmetric Matrices.

1971 • 35 citations

Row-column permutation of sparse matrices

1967 • 34 citations

THE SPARSE TABLEAU APPROACH TO FINITE ELEMENT ASSEMBLY

1976 • 34 citations

A Description of Strengthening and Weakening Members of a Group

1959 • 34 citations

Iterative methods for linear least squares problems.

1974 • 34 citations

An algorithm for the blocks and cutnodes of a graph

1971 • 33 citations

The Solution of Large Symmetric Eigenproblems by Sectioning

1972 • 33 citations

On the Reduction of Sparse Matrices to Condensed Forms by Similarity Transformations

1975 • 33 citations

Eigenproblems for Matrices Associated with Periodic Boundary Conditions

1977 • 33 citations

On the Product Form of Inverses of Sparse Matrices

1966 • 32 citations

The Product Form of Inverses of Sparse Matrices and Graph Theory

1967 • 32 citations

Computer Implementation of the Finite-Element Procedure

1973 • 32 citations

Connectivity and Reducibility of Graphs

1962 • 32 citations

A BIBLIOGRAPHICAL TOUR OF THE LARGE, SPARSE GENERALIZED EIGENVALUE PROBLEM

1976 • 31 citations

On the solution of large, structured linear complementarity problems: III.

1974 • 31 citations

A Note on the Least Squares Solution of a Band System of Linear Equations by Householder Reductions

1967 • 31 citations

On the Consistency of Precedence Matrices

1960 • 31 citations

Some Experiments on Sparse Sets of Linear Equations

1973 • 31 citations

A note on multiplying Boolean matrices

1962 • 31 citations

Row elimination for solving sparse linear systems and least squares problems

1976 • 31 citations

A graph technique for inverting certain matrices

1965 • 31 citations

Exploiting problem characteristics in the sparse matrix approach to frequency domain analysis

1972 • 31 citations

Graphs and Matrices

1967 • 30 citations

Algorithm 408: a sparse matrix package (part I) [F4]

1971 • 30 citations

Sparse Matrix Approach to the Frequency Domain Analysis of Linear Passive Electrical Networks

1972 • 29 citations

Solution of Certain Large Sets of Equations on Pegasus using Matrix Methods

1959 • 29 citations

Hybrid sparse-matrix methods

1973 • 28 citations

Inversion of Modified Symmetric Matrices

1968 • 28 citations

Jacobi and Gauss–Seidel Methods for Nonlinear Network Problems

1969 • 28 citations

QR-factorization of partitioned matrices

1974 • 28 citations

User program performance in virtual storage systems

1973 • 28 citations

Computer-aided design, Part 1 enhancing convergence properties by the choice of output variable assignments in the solution of Sparse equation sets

1971 • 28 citations

On the inversion of sparse matrices

1962 • 28 citations

An error analysis of a method for solving matrix equations

1973 • 28 citations

Iterative Methods for Linear Equations with Symmetric Positive Definite Matrix

1961 • 28 citations

Structural Models: An Introduction to the Theory of Directed Graphs

1966 • 27 citations

Computations with Sparse Matrices

1970 • 27 citations

Theorems on the Analysis of Nonlinear Transistor Networks*

1970 • 26 citations

Computer-Aided Design, Part 2 An approach to convergence and tearing in the solution of sparse equation sets

1971 • 26 citations

An Iterative Least-Square Method Suitable for Solving Large Sparse Matrices

1963 • 26 citations

Note on minimizing the bandwidth of sparse, symmetric matrices

1973 • 25 citations

Matrix Methods of Structural Analysis

1962 • 25 citations

An economical method for determining the smallest eigenvalues of large linear systems

1971 • 24 citations

Pseudo-Boolean Methods for Bivalent Programming

1966 • 24 citations

Optimal elimination for sparse symmetric systems as a graph problem.

1968 • 24 citations

ALGOL W reference manual

1972 • 24 citations

Solution of a system of simultaneous linear equations with a sparse coefficient matrix by elimination methods

1967 • 24 citations

An algorithm for solving a special class of tridiagonal systems of linear equations

1969 • 23 citations

An algorithm for computing all paths in a graph

1966 • 23 citations

The Analysis of Large Structural Systems

1960 • 23 citations

Computer program for solution of large, sparse, unsymmetric systems of linear equations

1973 • 23 citations

Essays on the Structure of Social Science Models

1964 • 23 citations

Topics in Numerical Analysis II

1975 • 22 citations

Iterative Eigenvalue Algorithms for Large Symmetric Matrices

1974 • 22 citations

Dynamic Storage and Retrieval in Sparsity Programming

1970 • 22 citations

A language for treating graphs

1970 • 22 citations

The Role of Partitioning in the Numerical Solution of Sparse Systems

1972 • 21 citations

Gradient methods for finite-element eigenproblems.

1969 • 21 citations

Projection Methods for Solving Sparse Linear Systems

1969 • 21 citations

On a programming language for graph algorithms

1972 • 21 citations

Improved Loss Formula Computation by Optimally Ordered Elimination Techniques

1971 • 20 citations

The solution of natural frequency equations by relaxation methods

1948 • 20 citations

Applications of Graphs and Boolean Matrices to Computer Programming

1960 • 20 citations

A Direct Method for Generalized Matrix Inversion

1967 • 19 citations

Random matrices and graphs

1966 • 19 citations

A Method of Solving Very Large Physical Systems in Easy Stages

1954 • 19 citations

A Theorem on Rank One Modifications to a Matrix and Its Inverse

1969 • 19 citations

An Elimination Method for the Solution of Linear Least Squares Problems

1973 • 18 citations

Structural Aspects of Large Dynamic Systems *

1975 • 18 citations

Deferment of computation in the method of least squares

1965 • 18 citations

Iterative eigenvalue algorithms based on convergent splittings

1975 • 17 citations

An operating environment for dynamic-recursive computer programming systems

1965 • 17 citations

On Directed Graph Solutions of Linear Algebraic Equations

1967 • 17 citations

On systems of linear equations of the form error analysis and certain consequences for structural applications

1974 • 16 citations

Solution of sparse indefinite systems of equations and least squares problems

1973 • 16 citations

On computing generalized inverses

1969 • 16 citations

A probabilistic approach to optimal pivoting and prediction of fill-in for random sparse matrices

1972 • 16 citations

Finite difference methods for surface waveguides

1970 • 16 citations

SPARSE MATRIX TECHNIQUES IN TWO MATHEMATICAL PROGRAMMING CODES

1969 • 16 citations

Degrees of Freedom and Modular Structure in Matrix Multiplication

1971 • 15 citations

Analysis of sparse systems

1972 • 15 citations

An analytic storage allocation model

1974 • 15 citations

SPARSE MATRIX SOFTWARE

1976 • 15 citations

Finite-element structural analysis

1977 • 15 citations

The Direct Solution of the Discrete Poisson Equation in $O(N^2 )$ Operations

1975 • 15 citations

On the number of nonzeros added when Gaussian elimination is performed on sparse random matrices

1974 • 15 citations

A Note on Fill for Sparse Matrices

1975 • 14 citations

Effective Ordering of Sparse Matrices Arising from Nonlinear Electrical Networks

1971 • 14 citations

Modifying Triangular Factors of the Basis in the Simplex Method

1972 • 14 citations

Automatic nested dissection

1974 • 14 citations

On Finding a Maximal Assignment

1966 • 14 citations

Implementation and analysis of efficient graph planarity testing algorithms

1969 • 14 citations

Nonserial dynamic programming: On the optimal strategy of variable elimination for the rectangular lattice

1972 • 14 citations

On Optimal-Pivoting Algorithms in Sparse Matrices

1972 • 14 citations

The implementation and use of sparse matrix techniques in general simulation programs

1974 • 14 citations

Perturbation Theory of the Normal Modes for an Exponential M-Curve in Non-Standard Propagation of Microwaves

1946 • 13 citations

Sorting and ordering sparse linear systems

1970 • 13 citations

Block Elimination on Finite Element Systems of Equations

1972 • 13 citations

An optimal pivoting order for the solution of sparse systems of equations

1974 • 13 citations

The Inversion of Sparse Matrices by a Strategy Derived from their Graphs

1967 • 13 citations

The numerical treatment of large eigenvalue problems

1974 • 12 citations

A sparse matrix scheme for the computer analysis of structures

1968 • 12 citations

On the intermediate eigenvalues of symmetric sparse matrices

1975 • 12 citations

A modified inversion procedure for product form of the inverse linear programming codes

1962 • 12 citations

PARTITIONING USING PAQ++This research was supported in part by the Office of Naval Research Grant N00014-67-A-0077-0021, by a National Science Foundation Graduate Fellowship and by Argonne National Laboratory.

1976 • 12 citations

On the orthonormalization of sparse vectors

1968 • 12 citations

Algorithm 183: reduction of a symmetric bandmatrix to triple diagonal form

1963 • 12 citations

BLOCK METHODS FOR SOLVING SPARSE LINEAR SYSTEMS

1976 • 11 citations

The Gaussian elimination and sparse systems

1968 • 11 citations

Relaxation methods for an eigenproblem

1966 • 11 citations

Deferment of Computation in the Method of Least Squares

1965 • 11 citations

SOR-Methods for the Eigenvalue Problem with Large Sparse Matrices

1974 • 11 citations

On the theory of the elimination process

1971 • 11 citations

Analysis of Sparse Elimination

1974 • 11 citations

An inversion method for band matrices

1970 • 11 citations

Maintaining a Sparse Inverse in the Simplex Method

1972 • 11 citations

Some results in the study of algorithms.

1971 • 10 citations

Application of Sparse Matrix Techniques in Reservoir Simulation

1973 • 10 citations

The Partitioning of Network Equations for Block Iteration

1966 • 10 citations

Solution of linear equations with coefficient matrix in band form

1968 • 10 citations

On the gaussian elimination method for inverting sparse matrices

1972 • 10 citations

Dissection of Structures

1967 • 9 citations

Eigenvalue Methods for Sparse Matrices

1972 • 9 citations

An Application of Regular Algebra to the Enumeration of Cut Sets in a Graph.

1974 • 9 citations

Pivoting-order computation method for large random sparse systems

1974 • 9 citations

Direct methods for solving elliptic difference equations

1971 • 9 citations

On the fill-in when sparse vectors are orthonormalized

1972 • 9 citations

A method of avoiding loss of accuracy in nodal analysis

1967 • 8 citations

Cookbook

1972 • 8 citations

A Method for Solving Large Matrix Equations Reduced From Fredholm Integral Equations of the Second Kind

1970 • 8 citations

CHEK and CHEKMAT: two chemical reaction kinetics programs

1974 • 8 citations

A New Iterative Procedure for the Solution of Sparse Systems of Linear Difference Equations

1972 • 7 citations

Arc graphs and their possible application to sparse matrix problems

1974 • 7 citations

The Crout reduction for sparse matrices

1969 • 7 citations

A computer-oriented representation of matrices

1970 • 7 citations

On diakoptics: Tearing an arbitrary system

1965 • 7 citations

Über das Gaußsche Eliminationsverfahren zur Invertierung dünn besetzter Matrizen

1972 • 7 citations

Application of Sparse Matrices to Analytical Photogrammetry

1972 • 6 citations

The application of sparse matrix methods to the numerical solution of nonlinear elliptic partial differential equations

1974 • 6 citations

Sparse Matrix Aspects of the Finite Element Method

1976 • 6 citations

A procedure for inverting large symmetric matrices

1962 • 6 citations

On the computation of selected eigenvalues

1966 • 6 citations

Fill-in comparisons between Gauss-Jordan and Gaussian eliminations

1974 • 6 citations

Ordering Systems of Equations

1961 • 6 citations

Hashing the subscripts of a sparse matrix

1974 • 6 citations

Letters to the Editors

1967 • 6 citations

Examples concerning efficient strategies for Gaussian elimination

1971 • 6 citations

A Comment on Matrix Inversion by Partition

1960 • 6 citations

Finding the inverse and connections of a type of large sparse matrix

1965 • 6 citations

A desirable form for sparse matrices when computing their inverse in factored forms

1973 • 5 citations

Decomposition of a graph into compactly connected two-terminal subgraphs

1971 • 5 citations

Equation-Solving Algorithms for the Finite-Element Method

1973 • 5 citations

On the reduction of a sparse matrix to hessenberg form

1968 • 5 citations

On the transformation of symmetric sparse matrices to the triple diagonal form

1968 • 5 citations

Computing with sparse matrices

1973 • 5 citations

Information representation and manipulation in a computer

1974 • 5 citations

Eigenvalue problem for large sparse matrices.

1973 • 5 citations

On the optimal choice of pivots for the Gaussian elimination

1972 • 5 citations

Non-linear networks and boundary value problems

1962 • 4 citations

A note on multiplying boolean matrices II

1964 • 4 citations

Some Results Concerning the Reduction of Binary Matrices

1971 • 4 citations

A note on a paper by Spillers and Hickerson

1971 • 4 citations

Effect of data representation on efficiency of sparse matrix operations.

1975 • 3 citations

Remarks on Solutions of the Optimal Assignment Problem

1963 • 3 citations

Algorithms: Algorithm 319: Triangular factors of modified matrices

1968 • 2 citations

Least Squares Successive Relaxation

1975 • 2 citations

Permutation of Irreducible Sparse Matrices to Upper Triangular Forms

1972 • 2 citations

Proceedings of the Symposium on Sparse Matrices and Their Applications

1970 • 2 citations

Application of the Finite Element Method to Regional Water Transport Phenomena

1972 • 2 citations

Graal — a Graph Algorithmic Language

1972 • 2 citations

Solution of large sparse systems of nonlinear equations

1975 • 2 citations

Single-Element Tearing and Modification of Sparse Symmetric Systems.

1972 • 2 citations

Tecniche di riordinamento delle equazioni per la risoluzione dei sistemi lineari sparsi

1972 • 2 citations

Hashing matrix subscripts

1975 • 1 citations

Generalized view of a Data Base

1972 • 1 citations

Operations on directed graphs.

1971 • 1 citations

Deleted Work

1955 • 0 citations