Applied Orthogonal Polynomials

该项目致力于发展正交多项式的构造性理论，并将其应用于数值求积和逼近理论中的具体问题。这包括在复平面上生成关于厄米特和非厄米特内积的正交多项式的构造方法，从正交多项式满足的递推关系恢复度量这种递推关系的稳定性，高斯和高斯-克朗罗德求积的构造方法，包括误差分析，以及一般正交多项式在分段多项式函数保矩逼近和约束多项式最小二乘逼近中的应用。

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.