Sparse Sets Of Linear Equations Research Articles

On Some Pivotal Strategies in Gaussian Elimination by Sparse Technique

Pivotal interchanges are commonly used in the solution of large and sparse systems of linear algebraic equations by Gaussian elimination (in order to preserve the sparsity of the matrix and to prevent the appearance of large roundoff errors during the computations). The Markowitz strategy (see [H. M. Markowitz, The elimination form of inverse and its applications to linear programming, Management Sci., 3 (1957), pp. 255–269]) is often used to determine the pivotal sequence. An efficient implementation of this strategy is given by Curtis and Reid (see [A. R. Curtis and J. K. Reid, Fortran subroutines for the solution of sparse sets of linear equations, A.E.R.E., Report R.6844, HMSO, London, 1971]) and improved by Duff (see [I. S. Duff, MA28—a set of Fortran subroutines for sparse unsymmetric matrices, A.E.R.E., Report R.8730, HMSO, London, 1977]). In this paper it is shown how the classical Markowitz idea can be generalized. Consider the following parameters: u —the stability factor and $p(s)$—the number o...

Method of implicit non-stationary iteration for solving neutron diffusion linear equations

Solution of the set of sparse linear equations arising from numerical approximation to elliptic operators is possible using the method of successive line over-relaxation (SLOR). An alternative approach is introduced, the method of implicit non-stationary iteration (MINI), which, although no faster on a computer than SLOR for 2D reactor neutronic calculations, does offer a likely time saving for 3D reactor calculations. Steady state and kinetic calculations are reported for some real reactor problems.

Large Sparse Sets of Linear Equations

Large Sparse Sets of Linear Equations

The calculation of steady state incompressible flow in large networks of pipes

A method of linearisation is described which enables the calculation of the steady state flow in networks of pipes and pumps handling an incompressible fluid. In an Appendix a numerical method is outlined for the repeated solution of large sparse sets of linear equations.

Some Experiments on Sparse Sets of Linear Equations

This paper describes five pivot selection algorithms in inversion of a large sparse matrix when using the method of Gaussian elimination. Some numerical experiments are presented.Since the pivots are chosen partly on the basis of element magnitudes, it is assumed that all the matrix elements are of comparable size and two scaling algorithms are discussed based on the assumption that the given matrix can be scaled to this form.

Large Sparse Sets of Linear Equations

Large Sparse Sets of Linear Equations

Large Sparse Sets of Linear Equations

Large Sparse Sets of Linear Equations