Hermite continuation and numerical bifurcation analysis.

机译：Hermite延续和数值分支分析。

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The methods of Hermite continuation, bisection-like branch switching, location by intermediate correction, parallel methods and smooth test functions are presented. A computational comparison of the method shows that Hermite continuation is a faster method for continuation for systems of large dimension. The bisection-like branch switching method outperforms other existing methods. The use of smooth test functions for the detection of singularities with polynomial interpolation allows sufficient guesses for singularity locators with large step sizes. These test functions are more computationally stable when compared to existing test functions. Parallelized methods are compared, showing that singularity location can benefit from a parallel method.

机译：提出了Hermite延续，两等分分支切换，中间校正定位，并行方法和平滑测试功能的方法。该方法的计算比较表明，对于大型系统，Hermite连续是一种更快的连续方法。二等分分支切换方法优于其他现有方法。使用平滑测试功能通过多项式插值法检测奇点时，可以对步长较大的奇点定位器进行充分的猜测。与现有测试功能相比，这些测试功能在计算上更加稳定。比较了并行方法，表明奇异位置可以从并行方法中受益。

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作者
Hughes, Jeremy S.;
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作者单位

The University of Alabama in Huntsville.;

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授予单位 The University of Alabama in Huntsville.;
学科 Applied Mathematics.;Computer Science.
学位 Ph.D.
年度 2010
页码 109 p.
总页数 109
原文格式 PDF
正文语种 eng
中图分类 TS97-4;
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Hermite continuation and numerical bifurcation analysis.

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