کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
518430 | 867587 | 2014 | 22 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: 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](/preview/png/518430.png)
The first purpose of this paper is to provide further illustrations, from both theoretical and numerical perspectives, for the nonconvergence of h-refinement in hp-approximation by the prolate spheroidal wave functions (PSWFs), a surprising convergence property that was first discovered by Boyd et al. (2013) [3]. The second purpose is to offer a new basis that leads to prolate-collocation systems with condition numbers independent of (c,N)(c,N), the intrinsic bandwidth parameter and the number of collocation points. We highlight that the collocation scheme together with a very practical rule for pairing up (c,N)(c,N) significantly outperforms the Legendre polynomial-based method (and likewise other Jacobi polynomial-based methods) in approximating highly oscillatory bandlimited functions.
Journal: Journal of Computational Physics - Volume 268, 1 July 2014, Pages 377–398