Fast algorithms for Jacobi expansions via nonoscillatory phase functions
Fast algorithms for Jacobi expansions via nonoscillatory phase functions
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DOI：
10.1093/imanum/drz016
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发表时间：
2018-03
影响因子：
2.1
通讯作者：
J. Bremer;Haizhao Yang
中科院分区：
文献类型：
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作者：
J. Bremer;Haizhao Yang
我们描述了一套快速算法，用于评估雅可比多项式，应用相应的离散Sturm-Liouville特征变换和计算Gauss-Jacobi求积规则。我们的方法，适用于在雅可比的微分方程中的参数$\alpha $和$\beta $的幅度小于$1/2$的情况下，是基于众所周知的事实，即在这个制度雅可比的微分方程承认一个非振荡相函数，可以通过一个仿射函数在其域的大部分松散近似。我们用几个数值实验来说明这一点，其源代码是公开的。
We describe a suite of fast algorithms for evaluating Jacobi polynomials, applying the corresponding discrete Sturm–Liouville eigentransforms and calculating Gauss–Jacobi quadrature rules. Our approach, which applies in the case in which both of the parameters $\alpha $ and $\beta $ in Jacobi’s differential equation are of magnitude less than $1/2$, is based on the well-known fact that in this regime Jacobi’s differential equation admits a nonoscillatory phase function that can be loosely approximated via an affine function over much of its domain. We illustrate this with several numerical experiments, the source code for which is publicly available.