Rational Gauss quadrature formulas try to achieve the same kind of properties but the polynomials are replaced by rational functions with a set of pre-fixed poles. n j=1(1 − z/αj). is thus a special case. We shall consider the properties and computation of these quadrature formulas.
Efficient algorithms for computing the nodes and weights of an n-point. Gauss rule use the n × n symmetric tridiagonal matrix determined by the recursion ...
Traditionally, Gauss quadrature rules are designed to integrate exactly polynomi- als of maximum possible degree. This is meaningful for integrand functions ...
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This paper describes how banded matrices determined by the recursion coefficients for these orthonormal rational functions can be used to efficiently compute ...
May 28, 2022 · We discuss the use of rational Gauss-type quadrature rules to approximate the integral (1.5). This is useful when the matrix A is large and the ...
This paper describes how banded matrices determined by the recursion coefficients for these orthonor mal rational functions can be used to efficiently compute ...
The application of rational Gauss rules, instead of standard Gauss rules, is beneficial when the function f has singularities close to the spectrum of A.
Jul 20, 1993 · We describe two methods for generating such quadrature rules numerically and report on computational experience with them.
Rational Gauss quadrature rules that are designed to exactly integrate Laurent polynomials with a fixed pole in the vicinity of the support of the measure may ...
We present three types of reccurence relations for orthogonal rational functions with arbitrary real and/or complex conjugate poles and their ap-.