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Parallel Factorizations in Numerical Analysis
Pierluigi Amodio,Luigi Brugnano +1 more
TL;DR: In this article, the parallel solution of sparse linear systems, usually deriving by the discretization of ODE-IVPs or ODE BVPs, is reviewed.
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Abstract: In this paper we review the parallel solution of sparse linear systems, usually deriving by the discretization of ODE-IVPs or ODE-BVPs. The approach is based on the concept of parallel factorization of a (block) tridiagonal matrix. This allows to obtain efficient parallel extensions of many known matrix factorizations, and to derive, as a by-product, a unifying approach to the parallel solution of ODEs.
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References
A collection of problems for which Gaussian elimination with partial pivoting is unstable
TL;DR: A significant collection of two-point boundary value problems is shown to give rise to linear systems of algebraic equations on which Gaussian elimination with row partial pivoting is unstable when standard solution techniques are used.
80
Alternate Row and Column Elimination for Solving Certain Linear Systems
TL;DR: In this paper, the authors show how to solve linear systems with a certain block structure in a stable manner, without introducing any extraneous elements, by alternate row and column elimination.
62
Optimized cyclic reduction for the solution of linear tridiagonal systems on parallel computers
TL;DR: The obtained speedups show that this is the best possible parallel implementation of the cyclic reduction and one of the fastest algorithms for the solution of tridiagonal systems on a parallel computer with medium grain parallelism.
11
A survey of parallel direct methods for block bidiagonal linear systems on distributed memory computers
TL;DR: Four parallel algorithms for the solution of block bidiagonal linear systems on distributed memory computers are presented and the results of experiments with the four algorithms implemented in Parallel Fortran on a linear array of 32 Transputers are presented.
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