Mathematical Sciences: Pade and Other Rational Approximation; Moment Theory

数学科学：Pade 和其他有理逼近；

• 批准号: 8700498
• 负责人: William Jones
• 金额: $ 8.77万
• 依托单位: University of Colorado at Boulder
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-06-15 至 1989-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8700498&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Pade; Other; Rational

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.

该项目将重点研究复杂域中的有理插值和逼近问题。 重点将放在帕德近似和相关的连分数上。 将开发复杂分析的构造方法来研究收敛性、收敛速度、收敛加速度、截断误差分析、矩理论和稳定性分析。 数值分析和大规模计算方法将用于数值实验（以获得对复杂问题的新见解）和特殊函数计算的数值结果。 这项工作涉及基础数学分析及其在数字滤波和信号处理、特殊函数理论以及非线性 Riccati 微分方程求解中的应用。 数字信号处理广泛应用于天文学、经济学、电力规划、医学、雷达、地震学和语音处理等领域。 预计该项目将显着增加目前有理逼近的知识水平，并为未来的研究指出新的方向。