论文标题
非线性特征值问题的随机草图
Randomized sketching of nonlinear eigenvalue problems
论文作者
论文摘要
理性近似是获得易于评估和线性化的非线性函数的准确替代物的强大工具。插值自适应的Antoulas-Anderson（AAA）方法是一种数值构造此类近似值的方法。但是，对于大规模矢量和矩阵值函数，AAA的设置值变体的直接应用变得效率低下。我们提出并分析了一种称为SketchaaA的功能的新草图方法，该方法具有很高的概率，可导致比以前建议的方法更好的近似值，同时保持效率。素描方法以黑盒方式起作用，其中仅需要在采样点上对非线性功能的评估。具有非线性特征值问题的数值测试说明了我们方法的疗效，高于200以上的加速度对大规模黑盒功能进行采样而不牺牲准确性。
Rational approximation is a powerful tool to obtain accurate surrogates for nonlinear functions that are easy to evaluate and linearize. The interpolatory adaptive Antoulas--Anderson (AAA) method is one approach to construct such approximants numerically. For large-scale vector- and matrix-valued functions, however, the direct application of the set-valued variant of AAA becomes inefficient. We propose and analyze a new sketching approach for such functions called sketchAAA that, with high probability, leads to much better approximants than previously suggested approaches while retaining efficiency. The sketching approach works in a black-box fashion where only evaluations of the nonlinear function at sampling points are needed. Numerical tests with nonlinear eigenvalue problems illustrate the efficacy of our approach, with speedups above 200 for sampling large-scale black-box functions without sacrificing on accuracy.
