Jonathan D. Hauenstein , Caroline Hills , Andrew J. Sommese, Charles W. Wampler
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引用次数: 0
Abstract
Homotopy continuation is a standard method used in numerical algebraic geometry for solving multivariate systems of polynomial equations. Techniques such as the so-called gamma trick yield trackable homotopies with probability one. However, since numerical algebraic geometry employs numerical path tracking methods, being close to a branch point may cause concern with finite precision computations. This paper provides a systematic study of branch points of homotopies to elucidate how branch points are distributed and use this information to study the probability of failure when using finite precision. Several examples, including a system arising in kinematics, with various start systems are included to demonstrate the theoretical analysis.
期刊介绍：
Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results.
In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.
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