On hp-convergence of prolate spheroidal wave functions and a new well-conditioned prolate-collocation scheme
On hp-convergence of prolate spheroidal wave functions and a new well-conditioned prolate-collocation scheme
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DOI：
10.1016/j.jcp.2014.03.005
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发表时间：
2013-10
期刊：
影响因子：
--
通讯作者：
Lilian Wang;Jing Zhang;Zhimin Zhang
中科院分区：
文献类型：
--
作者：
Lilian Wang;Jing Zhang;Zhimin Zhang
本文的第一个目的是提供一个严格的证明的非收敛的PSWFs，一个令人惊讶的收敛特性，首先观察到的博伊德等人[J.科学。计算：2013年]。第二个目的是提供一个新的基础，导致谱配置系统的条件数独立于固有带宽参数和配置点的数量。此外，这项工作提供了见解的发展，有效的频谱算法使用这种非多项式的基础。我们特别强调，搭配方案连同一个非常实用的配对规则，在逼近高振荡带限函数方面，显着优于基于勒让德多项式的方法（以及其他基于雅可比多项式的方法）。
The first purpose of this paper is to provide a rigorous proof for the nonconvergence of-refinement in-approximation by the PSWFs, a surprising convergence property that was first observed by Boyd et al [J. Sci. Comput., 2013]. The second purpose is to offer a new basis that leads to spectral-collocation systems with condition numbers independent ofthe intrinsic bandwidth parameter and the number of collocation points. In addition, this work gives insights into the development of effective spectral algorithms using this non-polynomial basis. We in particular highlight that the collocation scheme together with a very practical rule for pairing upsignificantly outperforms the Legendre polynomial-based method (and likewise other Jacobi polynomial-based method) in approximating highly oscillatory bandlimited functions.