A Software Repository for Gaussian Quadratures and Christoffel Functions

This companion piece to the author s 2018 book, A Software Repository for Orthogonal Polynomials, focuses on Gaussian quadrature and the related Christoffel function. The book makes Gauss quadrature rules of any order easily accessible for a large variety of weight functions and for arbitrary precision. It also documents and illustrates known as well as original approximations for Gauss quadrature weights and Christoffel functions. The repository contains 60+ datasets, each dealing with a particular weight function. Included are classical, quasi-classical, and, most of all, nonclassical weight functions and associated orthogonal polynomials. Scientists, engineers, applied mathematicians, and statisticians will find the book of interest.

Walter Gautschi was a research mathematician at the National Bureau of Standards in Washington, D.C., and at Oak Ridge National Laboratory before taking on a full professorship at Purdue University, where he remained until his retirement in 2000. Previously he held postdoctoral positions at the Istituto Nazionale per le Applicazioni del Calcolo (INAC) in Rome and at Harvard University. Elected Corresponding Member of the Bavarian Academy of Sciences and Foreign Member of the Turin Academy of Sciences, Gautschi has served on the editorial committees of several journals and was chairman of the Mathematics of Computation editorial board. He has published extensively in the areas of computational mathematics, orthogonal polynomials, and history, including two books.