## The Efficient Parallel Iterative Solution Of Large Sparse Linear Systems (1992)

Citations: | 8 - 0 self |

### BibTeX

@MISC{Jones92theefficient,

author = {Mark T. Jones and Paul E. Plassmann},

title = {The Efficient Parallel Iterative Solution Of Large Sparse Linear Systems},

year = {1992}

}

### OpenURL

### Abstract

The development of efficient, general-purpose software for the iterative solution of sparse linear systems on a parallel MIMD computer requires an interesting combination of expertise. Parallel graph heuristics, convergence analysis, and basic linear algebra implementation issues must all be considered. In this paper, we discuss how we have incorporated recent results in these areas into a general-purpose iterative solver. First, we consider two recently developed parallel graph coloring heuristics. We show how the method proposed by Luby, based on determining maximal independent sets, can be modified to run in an asynchronous manner and give an expected running time bound for this modified heuristic. In addition, a number of graph reduction heuristics are described that are used in our implementation to improve the individual processor performance. The effect of these various graph reductions on the solution of sparse triangular systems is categorized. Finally, we discuss the perform...

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Citation Context ...l mode. We use a shifted, inverted variant of the Lanczos algorithm to solve this eigenproblem [16]. This method has been shown to be very efficient for the parallel solution of the vibration problem =-=[9]-=-. Again, the major computational task is the solution of large sparse systems of linear equations. The three-dimensional finite element grid needed to model the crystals is much more refined in the le... |

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Citation Context ... withsmatrix products once the partitioned inverse is formed. We note that this can always done with a pointwise coloring, wheresis the number of colors used. It has been observed by Robert Schreiber =-=[18] that-=- the partitioned inverse approach can reduce the steps in pointwise coloring approach by a factor of two. Suppose two colors are used. We write the pointwise system as L = " D 1;1 0 L 2;1 D 2;2 #... |