A Parallel Endgame
A Parallel Endgame
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平行的结局
DOI：
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发表时间：
2010
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通讯作者：
A. Sommese
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文献类型：
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作者：
Daniel J. Bates;J. Hauenstein;A. Sommese
数值代数几何是致力于通过数值方法求解和操纵多项式系统的领域，数值方法主要基于连续性。由于连续性的极端内在并行性，可以成功处理比其他方法大得多的多项式系统。奇异解需要称为残局的特殊数值方法，而当前使用的残局没有利用并行性。本文概述了并行计算背景下的延续和残局。我们还介绍了一种基于柯西残局的新颖并行算法，用于在同伦路径末端执行残局，以及在其实现中有用的一些启发式算法。该方法已在 Bertini 软件包中实施，可显着提高效率。
Numerical algebraic geometry is the area devoted to the solution and manipulation of polynomial systems by numerical methods, which are mainly based on continuation. Due to the extreme intrinsic parallelism of continuation, polynomial systems may be successfully dealt with that are much larger than is possible with other methods. Singular solutions require special numerical methods called endgames, and the endgames currently used do not take advantage of parallelism. This article gives an overview of continuation and endgames in the context of parallel computation. We also introduce a novel parallel algorithm for performing endgames at the end of homotopy paths, based on the Cauchy endgame, along with some heuristics useful in its implementation. This method, which has been implemented in the Bertini software package, leads to a significant gain in efficiency.