Orthogonal Polynomials: Computation and Approximation

This is the first book on constructive methods for and applications of orthogonal polynomials, and the first available collection of relevant Matlab codes. The book begins with a concise introduction to the theory of orthogonal polynomials on the real line (or part thereof) relative to a positive measure of integration and topics, which are particularly relevant to computation. The second chapter develops computational methods for generating coefficients in the basic three-term recurrence relation, including moment-based methods and discretization methods. Other miscellaneous methods are also discussed, including computation of Cauchy integrals, modification algorithms for underlying measures, and computation of orthogonal polynomials of the Sobolev type. The final chapter deals with selected applications: numerical evaluation of integrals (in particular the Gauss-type quadrature methods), polynomial least squares approximation, moment-preserving spline approximation, and the summation of slowly convergent series. Detailed historic and bibliographic notes are appended to each chapter. The book will be of interest not only to mathematicians and numerical analysts but also to a wide range of scientists and engineers

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