By Walter Gautschi
This can be the 1st e-book on optimistic equipment for, and purposes of orthogonal polynomials, and the 1st to be had selection of proper Matlab codes. The booklet starts with a concise advent to the idea of polynomials orthogonal at the genuine line (or a element thereof), relative to a favorable degree of integration. subject matters that are relatively proper to computation are emphasised. the second one bankruptcy develops computational equipment for producing the coefficients within the uncomplicated three-term recurrence relation. The tools are of 2 types: moment-based equipment and discretization equipment. the previous are supplied with a close sensitivity research. different subject matters addressed crisis Cauchy integrals of orthogonal polynomials and their computation, a brand new dialogue of amendment algorithms, and the iteration of Sobolev orthogonal polynomials. the ultimate bankruptcy offers with chosen purposes: the numerical assessment of integrals, specially by way of Gauss-type quadrature tools, polynomial least squares approximation, moment-preserving spline approximation, and the summation of slowly convergent sequence. unique historical and bibliographic notes are appended to every bankruptcy. The e-book could be of curiosity not just to mathematicians and numerical analysts, but additionally to a large customers of scientists and engineers who understand a necessity for making use of orthogonal polynomials.