Applied Orthogonal Polynomials

该项目涉及一种建设性理论的发展 正交多项式及其应用于具体问题 数值积分和逼近理论。 这包括 正交多项式的构造方法 复平面相对于厄米特以及非厄米特内 产品，从递归关系恢复测量 满足正交多项式，这种递归的稳定性 关系，高斯和高斯-克朗罗德的构造性方法 求积法，包括误差分析和求积法的应用 一般正交多项式的矩保持逼近 分段多项式函数与约束多项式最小 平方近似

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.