Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Multilevel k-way partitioning scheme for irregular graphs
Journal of Parallel and Distributed Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
P3VI: a partitioned, prioritized, parallel value iterator
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Fast iterative graph computation with block updates
Proceedings of the VLDB Endowment
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We describe a new algorithm designed to quickly and robustly solve general linear problems of the form Ax = b. We describe both serial and parallel versions of the algorithm, which can be considered a prioritized version of an Alternating Multiplicative Schwarz procedure. We also adopt a general view of alternating Multiplicative Schwarz procedures which motivates their use on arbitrary problems (even which may not have arisen from problems that are naturally decomposable) by demonstrating that, even in a serial context, algorithms should use many, many partitions to accelerate convergence; having such an over-partitioned system also allows easy parallelization of the algorithm, and scales extremely well. We present extensive empirical evidence which demonstrates that our algorithm, with a companion subsolver, can often improve performance by several orders of magnitude over the subsolver by itself and over other algorithms.