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Solution of linear systems of equations: Direct methods for finite element problems

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1007/978-1-4615-8675-3openalex-snapshot

Sparse Matrices and their Applications

inferredcites →https://doi.org/10.1007/978-1-4615-8675-3_14openalex-snapshot

Several Strategies for Reducing the Bandwidth of Matrices

inferredcites →https://doi.org/10.1007/978-3-642-85972-4_1openalex-snapshot

Sparse Matrix Aspects of the Finite Element Method

inferredcites →https://doi.org/10.1007/bf02521587openalex-snapshot

Reducing the profile of sparse symmetric matrices

inferredcites →https://doi.org/10.1016/0045-7949(75)90016-4openalex-snapshot

Solution of linear equations with skyline-stored symmetric matrix

inferredcites →https://doi.org/10.1016/0309-1708(80)90069-xopenalex-snapshot

An analysis of the finite element method

inferredcites →https://doi.org/10.1061/jsdeag.0001768openalex-snapshot

Dissection of Structures

inferredcites →https://doi.org/10.1061/jsdeag.0003559openalex-snapshot

Solution of Linear Equations—State-of-the-Art

inferredcites →https://doi.org/10.1093/comjnl/9.3.281openalex-snapshot

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

inferredcites →https://doi.org/10.1137/0710032openalex-snapshot

Nested Dissection of a Regular Finite Element Mesh

inferredcites →https://doi.org/10.1137/0711050openalex-snapshot

On Block Elimination for Sparse Linear Systems

inferredcites →https://doi.org/10.1137/0712035openalex-snapshot

A Note on Fill for Sparse Matrices

inferredcites →https://doi.org/10.1137/0713020openalex-snapshot

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

inferredcites →https://doi.org/10.1137/0713023openalex-snapshot

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

inferredcites →https://doi.org/10.1137/0713056openalex-snapshot

On George’s Nested Dissection Method

inferredcites →https://doi.org/10.1137/0714011openalex-snapshot

Numerical Experiments Using Dissection Methods to Solve n by n Grid Problems

inferredcites →https://doi.org/10.1137/0715021openalex-snapshot

Algorithms for Matrix Partitioning and the Numerical Solution of Finite Element Systems

inferredcites →https://doi.org/10.1137/1003021openalex-snapshot

The Use of Linear Graphs in Gauss Elimination

inferredcites →https://doi.org/10.1145/800195.805928openalex-snapshot

Reducing the bandwidth of sparse symmetric matrices

inferredcites →https://doi.org/10.2307/1911908openalex-snapshot

The Theory of Graphs and Its Applications

inferredcites →https://doi.org/10.2307/2003558openalex-snapshot

The Algebraic Eigenvalue Problem

inferredcites →https://doi.org/10.2307/2005716openalex-snapshot

An Analysis of the Finite Element Method

inferredcites →https://doi.org/10.2307/2333777openalex-snapshot

The Theory of Graphs and its Applications.

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Perfect Elimination and Chordal Bipartite Graphs

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Ordering for Optimal Patterns of Structural Matrices: Graph Theory Methods

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Computer Solution of Systems of Linear Equations in Engineering Geodesy

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A method of solving nonlinear variational problems by nonlinear transformation of the objective functional. Part I

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A method of solving nonlinear variational problems by nonlinear transformation of the objective functional. Part II

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A cutting sequencing algorithm

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Treediagonal matrices and their inverses

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An interactive automatic mesh generator for the microcomputer

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Optimal pivot strategies for load-flow calculation

inferred← citeshttps://doi.org/10.1016/b978-0-12-068780-0.50012-1openalex-snapshot

Direct Methods for Solving Finite Element Equations

inferred← citeshttps://doi.org/10.1016/b978-0-12-289260-8.50019-4openalex-snapshot

Perfect Gaussian Elimination

inferred← citeshttps://doi.org/10.1016/b978-0-12-557580-5.50015-6openalex-snapshot

References

inferred← citeshttps://doi.org/10.1016/s0167-5060(04)80060-8openalex-snapshot

Perfect Gaussian Elimination

inferred← citeshttps://doi.org/10.1016/s0304-0208(08)71205-2openalex-snapshot

Direct Solution and Storage of Large Sparse Linear Systems

inferred← citeshttps://doi.org/10.1017/s0962492916000076openalex-snapshot

A survey of direct methods for sparse linear systems

inferred← citeshttps://doi.org/10.1090/s0025-5718-1980-0583501-0openalex-snapshot

Numerical Stability of Nested Dissection Orderings

inferred← citeshttps://doi.org/10.1090/s0025-5718-1980-0583502-2openalex-snapshot

The spectral transformation Lánczos method for the numerical solution of large sparse generalized symmetric eigenvalue problems

inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.001.0001openalex-snapshot

Direct Methods for Sparse Matrices

inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.002.0001openalex-snapshot

Glossary of Symbols

inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.002.0005openalex-snapshot

inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.002.0006openalex-snapshot

Preface

inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0001openalex-snapshot

Introduction

inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0002openalex-snapshot

Sparse matrices: storage schemes and simple operations

inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0003openalex-snapshot

Gaussian elimination for dense matrices: the algebraic problem

inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0004openalex-snapshot

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

inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0009openalex-snapshot

Orderings based on dissection

inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0010openalex-snapshot

Implementing Gaussian elimination without symbolic factorize

inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0011openalex-snapshot

Implementing Gaussian elimination with symbolic factorize

inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0012openalex-snapshot

Gaussian elimination using trees

inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0013openalex-snapshot

Graphs for symmetric and unsymmetric matrices

inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0014openalex-snapshot

The solve phase

inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0015openalex-snapshot

Other sparsity-oriented issues

inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.005.0001openalex-snapshot

Matrix and vector norms

inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.005.0002openalex-snapshot

Pictures of sparse matrices

inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.005.0003openalex-snapshot

Solutions to selected exercises

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Solution of three-dimensional, anisotropic, nonlinear problems of magnetostatics using two scalar potentials, finite and infinite multipolar elements and automatic mesh generation

inferred← citeshttps://doi.org/10.1137/0605051openalex-snapshot

Graph Coloring Using Eigenvalue Decomposition

inferred← citeshttps://doi.org/10.1137/0719011openalex-snapshot

Storage Requirements for Profile and Frontal Elimination

inferred← citeshttps://doi.org/10.1145/355993.355998openalex-snapshot

Implementation of the Gibbs-Poole-Stockmeyer and Gibbs-King Algorithms

inferred← citeshttps://doi.org/10.1145/582353.582388openalex-snapshot

Numerical database management system

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Numerical database management system

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Fundamental Study of the Fill-in Minimization Problem

inferred← citeshttps://doi.org/10.18926/15782openalex-snapshot

Dissection Method for a Regular Finite Element Mesh

inferred← citeshttps://doi.org/10.18926/15803openalex-snapshot

Bandwidth Minimization Algorithm for Finite Element Mesh

inferred← citeshttps://doi.org/10.21236/ada113104openalex-snapshot

Implementation of the Gibbs-Poole-Stockmeyer Algorithm and the Gibbs-King Algorithm.

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NEW REORDERING ALGORITHM FOR SKYLINE METHOD

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A STUDY ON THE EFFECTIVITY OF THE BAND MATRIX METHOD IN NUMERICAL ANALYSIS

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