Mathematical Sciences: Pade and Other Rational Approximation; Moment Theory

在这个项目中，主要研究人员将与 研究生在有理插值的主题， 复域上的Pade逼近和连分式。 这些主题与矩理论、正交 多项式，劳伦多项式和高斯求积。 的 主要研究人员和他们的学生将应用他们的 特殊函数的计算和问题的结果 在数字信号处理中。 有理逼近领域是最古老的领域之一 经典分析的领域，其中有许多重要的 与其他科学和工程领域的联系。 在这 项目主要研究人员将与毕业生 让学生学习多项式零点的位置， 开发求积公式，研究收敛性 连续分数的性质（Pade'逼近）和 确定给定数字信号中的隐藏周期。

In this project the principal investigators will work with graduate students on the subject of rational interpolation in the complex domain by Pade' approximants and continued fractions. These topics are intimately related to moment theory, orthogonal polynomials, Laurent polynomials and Gaussian quadrature. The principal investigators and their students will apply their results to the computation of special functions and to problems in digital signal processing. The field of rational approximation is one of the oldest areas of classical analysis and one with many important connections to other fields of science and engineering. In this project the principal investigators will work with graduate students to study the location of zeros of polynomials for use in developing quadrature formulas, studying the convergence properties of continued fractions (Pade' approximants) and determining hidden periodicities in a given digital signal.