Abstract
PARASPAR is a package for the solution of linear algebraic systems whose coefficient matrices are large and sparse. Linear least squares problems can also be treated by PARASPAR (using the method of augmentation). Both direct methods and preconditioned iterative procedures are used. The direct methods are based on the classical Gaussian elimination with three different pivotal strategies. The iterative methods used are a modified ORTHOMIN algorithm, CGS, BI-CGSTAB and TFQMR. The preconditioners for all iterative algorithms are calculated by using an approximate LU factorization, which is obtained by dropping small non-zero elements during the Gaussian elimination. If the preconditioners are not sufficiently accurate (and, therefore, the iterative process is either divergent or the convergence is very slow), then an attempt to increase the accuracy of the preconditioner can automatically be performed.KeywordsIterative MethodGaussian EliminationTriangular MatriceParallel TaskLinear Algebraic SystemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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