2021/11/14 by Rafeh Rehan, Rehan, Rafeh, James Bremer +1
Materials Science · Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Mathematics #Mathematical Analysis and Transform Methods #Numerical Analysis (math.NA) #Quantum Mechanics and Non-Hermitian Physics #Solid-state spectroscopy and crystallography #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2111.07510
openalex publication_date 2021/11/14 · openalex created_date 2022/11/27 · openalex updated_date 2026/07/28
In addition to being the eigenfunctions of the restricted Fourier operator,\nthe angular spheroidal wave functions of the first kind of order zero and\nnonnegative integer characteristic exponents are the solutions of a singular\nself-adjoint Sturm-Liouville problem. The running time of the standard\nalgorithm for the numerical evaluation of their Sturm-Liouville eigenvalues\ngrows with both bandlimit and characteristic exponent. Here, we describe a new\napproach whose running time is bounded independent of these parameters.\nAlthough the Sturm-Liouville eigenvalues are of little interest themselves, our\nalgorithm is a component of a fast scheme for the numerical evaluation of the\nprolate spheroidal wave functions developed by one of the authors. We\nillustrate the performance of our method with numerical experiments.\n