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A new friendly method of computing prolate spheroidal wave functions and wavelets

机译:计算长球面波函数和小波的一种新的友好方法

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Prolate spheroidal wave functions, because of their many remarkable properties leading to new applications, have recently experienced an upsurge of interest. They may be defined as eigenfunctions of either a differential operator or an integral operator (as observed by Slepian in the 1960s). There are various ways of calculating their values based on both approaches. The standard one uses an approximation based on Legendre polynomials, which, however, is valid only on a finite interval. An alternative, valid in a neighborhood of infinity, uses a Bessel function approximation. In this letter we present a new method based on an eigenvalue problem for a matrix operator equivalent to that of the integral operator. Its solution gives the values of these functions on the entire real line and is computationally more efficient.
机译:扁长球面波函数由于具有许多引人注目的特性而导致了新的应用,因此最近引起了人们的关注。它们可以定义为微分算子或积分算子的本征函数(如Slepian在1960年代所观察到的)。有两种方法可以基于这两种方法计算其值。标准之一使用基于勒让德多项式的近似值,但是,该近似值仅在有限间隔内有效。在无穷大附近有效的替代方法使用贝塞尔函数逼近。在这封信中,我们提出了一种基于特征值问题的新方法,该方法适用于与积分算子相等的矩阵算子。它的解决方案在整个实线上给出了这些函数的值,并且计算效率更高。

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