论文标题
在平行共享内存计算机上多项式同喻的一条路径的强大数值跟踪
Robust Numerical Tracking of One Path of a Polynomial Homotopy on Parallel Shared Memory Computers
论文作者
论文摘要
我们考虑了跟踪由平行共享内存计算机上的多项式同喻定义的一个解决方案路径的问题。我们的稳健路径跟踪器应用牛顿的方法序列来定位最接近的单数参数值。最重要的是，它计算同型在多项式的Hessians的奇异值，以估计到最近不同路径的距离。共同使用这些估计来计算适当的自适应步骤。对于n维问题，与常用的预测指标方法相比，稳健路径跟踪器的成本开销是O（n）。该成本开销可以通过并行共享内存计算机上的多线程程序降低。
We consider the problem of tracking one solution path defined by a polynomial homotopy on a parallel shared memory computer. Our robust path tracker applies Newton's method on power series to locate the closest singular parameter value. On top of that, it computes singular values of the Hessians of the polynomials in the homotopy to estimate the distance to the nearest different path. Together, these estimates are used to compute an appropriate adaptive stepsize. For n-dimensional problems, the cost overhead of our robust path tracker is O(n), compared to the commonly used predictor-corrector methods. This cost overhead can be reduced by a multithreaded program on a parallel shared memory computer.
