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.
