Prolate Spheroidal Wave Functions, Quadrature, and Interpolation
Abstract
Polynomials are one of principal tools of classical numerical analysis. When a function needs to be interpolated, integrated, differentiated, etc., it is assumed to be approximated by a polynomial of a certain fixed order (though the polynomial is almost never constructed explicitly), and a treatment appropriate to such a polynomial is applied. We introduce analogous techniques based on the assumption that the function to be dealt with is band-limited, and use the well-developed apparatus of Prolate Spheroidal Wave Functions to construct quadratures, interpolation and differentiation formulae, etc. for band-limited functions. Since band-limited functions are often encountered in physics, engineering, statistics, etc. the apparatus we introduce appears to be natural in many environments. Our results are illustrated with several numerical examples.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 27, 2000
- Accession Number
- ADA630173
Entities
People
- Huahua Xiao
- N. Yarvin
- Vladimir Rokhlin
Organizations
- Yale University