COSAM » Events » 2018 » April » DMS Colloquium: Gradimir V. Milovanovic

 DMS Colloquium: Gradimir V. Milovanovic Time: Apr 10, 2018 (04:00 PM) Location: Parker Hall 236 Details: Speaker: Gradimir V. Milovanovic, Serbian Academy of Sciences and Arts Title: Special Quadrature Processes for Summation of Slowly Convergent Series Abstract: Slowly convergent series  appear in many problems in mathematics, physics  and other  sciences. There are several numerical methods based on linear and nonlinear transformations (e.g., Cesàro-transformation,  Aitken $$\Delta^2$$-transformation, Wynn-Shanks $$\varepsilon$$-algorithm, $$E$$-algorithm, Levin's transformation,  $$\rho$$-algorithm, etc.). In this lecture  we present the so-called summation/integration methods, which are very efficient. Methods are based on certain transformations of sums to weighted integrals over the real line or the half-line and  on an application of special Gaussian quadrature formulas with respect to some non-classical weight functions (Bose-Einstein, Fermi-Dirac, hyperbolic weights, $$\ldots$$). For constructing such quadrature rules we use a recent progress in symbolic computation and variable-precision arithmetic, implemented through our Mathematica package “OrthogonalPolynomials.” Several interesting applications will also be presented.   Faculty host: Narendra K. Govil

Last updated: 03/29/2018