Solution of sparse systems of equations on multiprocessor architectures

1989 ◽  
pp. 31-94 ◽  
Author(s):  
Alan George
Keyword(s):  
Systems Of Equations ◽  
Multiprocessor Architectures ◽  
Sparse Systems

On Solution Algorithms for Large Sparse Systems of Normal Equations in Photogrammetry

1981 ◽  
Vol 35 (1) ◽  
pp. 37-51
Author(s):  
Franz Steidler
Keyword(s):  
Bundle Adjustment ◽  
Solution Technique ◽  
Systems Of Equations ◽  
Direct Solution ◽  
Band Matrices ◽  
Normal Equations ◽  
Simple Version ◽  
Solution Algorithms ◽  
Solution Methods ◽  
Sparse Systems

The question of which algorithm is most appropriate for the solution of normal equations with different structures has been investigated. The solution methods are a direct solution for banded and banded-bordered matrices, a special direct solution technique for arbitrary sparse systems of equations and the method of conjugate gradients. The algorithms have first been applied to photogrammetric bundle adjustment with self-calibration, which leads to a banded-bordered matrix of the normal equations, and secondly to calculations of digital height models that are generated by a simple version of the method of finite elements and which lead to band matrices.

A SOLVER OF LINEAR SYSTEMS OF EQUATIONS (REBSM) FOR LARGE-SCALE ENGINEERING PROBLEMS

2012 ◽  
Vol 09 (01) ◽  
pp. 1240011 ◽  
Author(s):  
XIAO-WEI GAO ◽  
LINGJIE LI
Keyword(s):  
Large Scale ◽  
Solution Method ◽  
Gaussian Elimination ◽  
Systems Of Equations ◽  
The Finite Element Method ◽  
Elimination Algorithm ◽  
Engineering Problems ◽  
Sparse Systems ◽  
Linear Systems Of Equations ◽  
Element Method

In this paper, a novel linear equation solution method is proposed based on a row elimination back-substitution method (REBSM). The elimination and back-substitution procedures are carried out on individual row levels. The advantage of the proposed method is that it is much faster and requires less storage than the Gaussian elimination algorithm and, therefore, is capable of solving larger systems of equations. The method is particularly efficient for solving band diagonal sparse systems with symmetric or nonsymmetric coefficient matrices, and can be easily applied to popular numerical methods, such as the finite element method and the boundary element method. Detailed Fortran codes and examples are given to demonstrate the robustness and efficiency of the proposed method.

Solving large sparse systems of equations in econometric models

1987 ◽  
Vol 6 (3) ◽  
pp. 167-180 ◽  
Author(s):  
F. J. Henk Don ◽  
Giampiero M. Gallo
Keyword(s):  
Econometric Models ◽  
Systems Of Equations ◽  
Sparse Systems ◽  
Large Sparse Systems

Integrated simulator for MEMS using FEM implementation in AHDL and frontal solver for large sparse systems of equations

1999 ◽  
Author(s):  
Zeljko Mrcarica ◽  
Vladimir Risojevic ◽  
Michel Lenczner ◽  
Mirko Jakovljevic ◽  
Vanco Litovski
Keyword(s):  
Systems Of Equations ◽  
Sparse Systems ◽  
Large Sparse Systems

scholarly journals A combinatorial problem related to sparse systems of equations

2016 ◽  
Vol 85 (1) ◽  
pp. 129-144
Author(s):  
Peter Horak ◽  
Igor Semaev ◽  
Zsolt Tuza
Keyword(s):  
Combinatorial Problem ◽  
Systems Of Equations ◽  
Sparse Systems

Conjugate direction relaxation solutions for 3-D magnetotelluric modeling

Geophysics ◽  
1993 ◽  
Vol 58 (7) ◽  
pp. 1052-1057 ◽  
Author(s):  
Randall L. Mackie ◽  
Theodore R. Madden
Keyword(s):  
Integral Equation ◽  
Sparse Matrix ◽  
Three Dimensional ◽  
Approximate Solutions ◽  
Systems Of Equations ◽  
Integral Equation Methods ◽  
Tremendous Amount ◽  
Sparse Systems ◽  
Differential Methods ◽  
Made In

In recent years, there has been a tremendous amount of progress made in three‐dimensional (3-D) magnetotelluric modeling algorithms. Much of this work has been devoted to the integral equation technique (e.g., Hohmann, 1975; Weidelt, 1975; Wannamaker et al., 1984; Wannamaker, 1991). This method has contributed significantly to our understanding of electromagnetic field behavior in 3-D models. However, some of the very earliest work in 3-D modeling concentrated on differential methods (e.g., Jones and Pascoe, 1972; Reddy et al., 1977). It is generally recognized that differential methods are better suited than integral equation methods to model arbitrarily complex geometries, and consequently this area has recently been receiving a great deal of attention (e.g., Madden and Mackie, 1989; Xinghua et al., 1991; Mackie et al., 1993; Smith, 1992, personnal communication). Differential methods lead to large sparse systems of equations to be solved for the unknown field values. It is possible to use relaxation algorithms to quickly obtain approximate solutions to these systems of equations without resorting to standard matrix inversion routines or sparse matrix solvers.

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