A fast hermite transform with applications to protein structure determination

Abstract

We discuss algorithms for a fast and stable approximation of the Hermite transform of a compactly supported function on the real line, attainable via an application of a fast algebraic algorithm for computing sums associated to a three-term relation. Trade-offs between approximation in bandwidth (in the Hermite sense) and size of the support region are addressed. Generalizations to any family of orthogonal polynomials are outlined. Applications to the determination of protein structure are discussed.