ACM SIGSAM Bulletin, Vol 40, No. 1, March 2006 SNCA 2006 Poster Abstracts Symbolic-Numeric Computation and Applications List of Abstracts AMS/SIAM Special Session at the Joint Mathematics Meetings, San Antonio, Texas Sunday 15 January 2006 Daniel J. Bates (University of Notre Dame): Adaptive Precision in Homotopy Continuation (joint work with Andrew J. Sommese and Charles W. Wampler). Over the past decade, many algorithms have been developed for the numerical irreducible decomposition of the solution sets of polynomial systems. These algorithms form the foundation of the eld of numerical algebraic geometry. At the crux of all such algorithms lies the technique of homotopy continuation, a method for numerical path-following. Homotopy continuation is straightforward and robust if the solution curves to be traced are not near singularities. However, in the presence of singularities, the necessary linear algebra operations grind to a halt due to a lack of numerical precision. Therefore, by increasing precision adaptively in such situations, one may have more success in path-tracking. In this talk, I will brie y describe the effects of ill-conditioning on homotopy continuation, a new technique involving adaptive precision path-tracking, and the implementation of this technique in the software package Bertini, which is
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Symbolic-numeric computation and applications: list of abstracts
Szanto, Agnes; Verschelde, Jan; Zeng, Zhonggang
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, Volume 40 (1)
Association for Computing Machinery – Mar 1, 2006
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