How to generate unknown orthogonal polynomials out of known orthogonal polynomials
Copyright policy )How to generate unknown orthogonal polynomials out of known orthogonal polynomials
The aim of this paper is to present algorithms for generating the three- term recursion coefficients of orthogonal polynomials for a weight function \(v(t)=r(t)w(t)\). The weight function is obtained by modifying a given weight function \(w\) by a rational function \(r\). The authors describe a modified Chebyshev algorithm and apply it to the construction of orthogonal polynomials. Three algorithms are presented for the computation of orthogonal polynomials relative to weight functions \(v\) obtained by modifying \(w\) by a linear divisor or by a quadratic divisor. Some experiments with the derived methods are presented and discussed.
- Universität Hamburg France
- Universität Hamburg Germany
- Universität Hamburg
- Institute of Applied Mathematics Russian Federation
- Stanford University United States
modified moments, recurrence relations, Orthogonal polynomials, Applied Mathematics, Gauss quadrature, algorithms, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Computational Mathematics, Computation of special functions and constants, construction of tables, Numerical methods for functional equations, modified Chebyshev algorithm, orthogonal polynomials
modified moments, recurrence relations, Orthogonal polynomials, Applied Mathematics, Gauss quadrature, algorithms, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Computational Mathematics, Computation of special functions and constants, construction of tables, Numerical methods for functional equations, modified Chebyshev algorithm, orthogonal polynomials
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).17 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!