scholarly journals Recurrence Coefficients of Orthogonal Polynomials with Respect to Some Self-Similar Singular Distributions

1995 ◽  
Vol 14 (1) ◽  
pp. 141-155 ◽  
Author(s):  
H.-J. Fischer
Keyword(s):  
Orthogonal Polynomials ◽  
Recurrence Coefficients ◽  
Self Similar

Orthogonal polynomials: applications and computation

Acta Numerica ◽  
1996 ◽  
Vol 5 ◽  
pp. 45-119 ◽  
Author(s):  
Walter Gautschi
Keyword(s):  
Numerical Methods ◽  
Weight Function ◽  
Orthogonal Polynomials ◽  
Rational Function ◽  
Recurrence Relations ◽  
Recurrence Coefficients ◽  
Basic Task ◽  
Sobolev Orthogonal Polynomials ◽  
Gauss Type ◽  
Three Term Recurrence Relation

We give examples of problem areas in interpolation, approximation, and quadrature, that call for orthogonal polynomials not of the classical kind. We then discuss numerical methods of computing the respective Gauss-type quadrature rules and orthogonal polynomials. The basic task is to compute the coefficients in the three-term recurrence relation for the orthogonal polynomials. This can be done by methods relying either on moment information or on discretization procedures. The effect on the recurrence coefficients of multiplying the weight function by a rational function is also discussed. Similar methods are applicable to computing Sobolev orthogonal polynomials, although their recurrence relations are more complicated. The paper concludes with a brief account of available software.

scholarly journals On the limit behavior of recurrence coefficients for multiple orthogonal polynomials

2006 ◽  
Vol 139 (1-2) ◽  
pp. 346-370 ◽  
Author(s):  
A.I. Aptekarev ◽  
V. Kalyagin ◽  
G. López Lagomasino ◽  
I.A. Rocha
Keyword(s):  
Orthogonal Polynomials ◽  
Limit Behavior ◽  
Recurrence Coefficients ◽  
Multiple Orthogonal Polynomials

Spectral transformations, self-similar reductions and orthogonal polynomials

1997 ◽  
Vol 30 (21) ◽  
pp. 7621-7637 ◽  
Author(s):  
Vyacheslav Spiridonov ◽  
Luc Vinet ◽  
Alexei Zhedanov
Keyword(s):  
Orthogonal Polynomials ◽  
Spectral Transformations ◽  
Self Similar
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