Parallel algorithms for direct solution of large systems of equations

2003 ◽  
Author(s):  
J.-S. Wang ◽  
N. Ida
Keyword(s):  
Parallel Algorithms ◽  
Systems Of Equations ◽  
Direct Solution ◽  
Large Systems

scholarly journals A method of accelerating stationary iterative methods for solving linear systems

1988 ◽  
Vol 30 (1) ◽  
pp. 1-23
Author(s):  
G. K. Robinson
Keyword(s):  
Quadratic Forms ◽  
Simple Technique ◽  
Linear Equations ◽  
Full Rank ◽  
Systems Of Equations ◽  
Linear Combinations ◽  
Simultaneous Linear Equations ◽  
Large Systems ◽  
Stationary Iterative Methods ◽  
Refined Version

AbstractThe speed of convergence of stationary iterative techniques for solving simultaneous linear equations may be increased by using a method similar to conjugate gradients but which does not require the stationary iterative technique to be symmetrisable. The method of refinement is to find linear combinations of iterates from a stationary technique which minimise a quadratic form. This basic method may be used in several ways to construct refined versions of the simple technique. In particular, quadratic forms of much less than full rank may be used. It is suggested that the method is likely to be competitive with other techniques when the number of linear equations is very large and little is known about the properties of the system of equations. A refined version of the Gauss-Seidel technique was found to converge satisfactorily for two large systems of equations arising in the estimation of genetic merit of dairy cattle.

Improved semi-local convergence of the Newton-HSS method for solving large systems of equations

2019 ◽  
Vol 98 ◽  
pp. 29-35
Author(s):  
Ioannis K. Argyros ◽  
Santhosh George ◽  
Alberto Magreñán
Keyword(s):  
Local Convergence ◽  
Systems Of Equations ◽  
Large Systems

EFFECT OF ELEVATED TEMPERATURE ON CONCRETE STRUCTURES BY BOUNDARY ELEMENTS

2012 ◽  
Vol 09 (01) ◽  
pp. 1240014 ◽  
Author(s):  
PETR P. PROCHAZKA ◽  
TAT S. LOK
Keyword(s):  
Elevated Temperature ◽  
Boundary Element Method ◽  
Nonlinear System ◽  
Time Dependent ◽  
System Of Equations ◽  
Systems Of Equations ◽  
Strongly Nonlinear ◽  
Strongly Nonlinear System ◽  
Long Time ◽  
Large Systems

Extreme elevation of temperature principally threatens tunnel linings and may cause fatal disaster; the recovery of it may take a long time and significant traffic troubles. System of equations is to be described and solution in terms of boundary element method (BEM) is suggested. Moreover, a technique of time-dependent eigenparameters enables one to apply parallel computations and converts the strongly nonlinear system to pseudo-linear one using the influence and polarization tensors. Consequently, instead of repeated solution of large systems of equations, the multiplication of pre-calculated influence matrices has to be carried out instead. In order to properly create the above-outlined procedure, internal cells are selected in the regions primarily connected by the change of temperature. Some examples follow the theory.

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.

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