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.
