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Rational interpolatory quadrature formulas on the interval.

Integrals are ubiquitous in exact sciences; they are important to physicists, engineers in all disciplines, mathematicians and statisticians. Hence literature on numerical integration is very extensive. Most methods for numerical integration on an interval [a,b] are based on interpolatory quadrature formulas. These are numerical approximations based on polynomial interpolation and of a special form . If the function f has singularities close to the interval, however, these numerical approximations may converge very slowly to the exact integral value for increasing values of n. To increase the speed of convergence, rational interpolation can be used instead, with the poles of the interpolatory rational function simulating the singularities of the function f. However, computing the nodes {xj, j=1..n} and weights {λj, j=1..n} in rational interpolatory quadrature formulas (RIQs) still requires a very large computational effort in most cases. The aim of this project is the development of a software routine to accurately and efficiently compute the nodes and weights in Gauss type RIQs and in RIQs with positive weights, based on (quasi) orthogonal rational functions.
Date:1 Oct 2009 →  31 Aug 2012
Keywords:Numerical integration, Rational quadrature formulas, Orthogonal rational functions
Disciplines:Applied mathematics in specific fields, Computer architecture and networks, Distributed computing, Information sciences, Information systems, Programming languages, Scientific computing, Theoretical computer science, Visual computing, Other information and computing sciences