An O(1) Algorithm for the Numerical Evaluation of the Prolate Spheroidal Wave Functions of Order 0
This work provides a constant-time algorithm for a previously computationally expensive special function evaluation, benefiting researchers in signal processing and numerical analysis.
The paper presents an O(1) algorithm for evaluating prolate spheroidal wave functions of order 0, eliminating the dependence on the degree n and bandlimit γ, with numerical experiments confirming its properties.
The standard algorithm for the numerical evaluation of the prolate spheroidal wave function $\mathsf{Ps}\hskip.05em{}_{n}(x;γ^2)$ of order $0$, bandlimit $γ> 0$ and characteristic exponent $n$ has running time which grows with both $n$ and $γ$. Here, we describe an alternate approach which runs in time independent of these quantities. We present the results of numerical experiments demonstrating the properties of our scheme, and we have made our implementation of it publicly available.