Mathematical Sciences: Pade and Other Rational Approximation; Moment Theory

这个项目将集中在合理的问题， 复数域中的插值和逼近。 重点 将置于Pade近似物和相关续 分数 复变函数分析的构造性方法 是为了研究收敛速度 加速收敛，截断误差分析，矩 理论和稳定性分析。 数值分析方法和 大规模的计算将用于数值计算， 实验（以获得对复杂问题的新见解）和 计算特殊函数的数值结果。 这项工作涉及基本的数学分析， 应用于数字滤波和信号处理， 特殊函数论与非线性问题的解 Riccati微分方程 数字信号处理在不同领域都有应用 例如天文学、经济学、电力规划， 医学、雷达、地震学和语音处理。 是 预计该项目将大大增加目前的 有理逼近知识现状，并指出新的 未来研究的方向。

This project will focus on problems of rational interpolation and approximation in the complex domain. Emphasis will be placed on Pade approximants and related continued fractions. Constructive methods of complex analysis will be developed for the study of convergence, speed of convergence, acceleration of convergence, truncation error analysis, moment theory and stability analysis. Methods of numerical analysis and large-scale computations will be used both for numerical experimentation (to gain new insight into complex problems) and for numerical results on the computation of special functions. The work involves fundamental mathematical analysis with applications to digital filtering and signal processing, to the theory of special functions and to the solution of nonlinear Riccati differential equations. Digital signal processing has applications to diverse areas such as astronomy, economics, electrical power planning, medicine, radar, seismology and speech processing. It is expected that the project will add significantly to the present state of knowledge of rational approximation and point out new directions for future research.