The project is concerned with the development of a constructive theory of orthogonal polynomials and their application to concrete problems in numerical quadrature and approximation theory. This includes constructive methods for generating orthogonal polynomials in the complex plane relative to Hermitian as well as non-Hermitian inner products, the recovery of the measure from the recurrence relation satisfied by orthogonal polynomials the stability of such recurrence relations, constructive methods for Gaussian and Gauss-Kronrod quadratures,including the analysis of errors, and applications of general orthogonal polynomials to moment-preserving approximation by piecewise polynomial functions and to constrained polynomial least squares approximation.
