scholarly journals Asymptotic Zero Distribution of Orthogonal Polynomials with Discontinuously Varying Recurrence Coefficients

2001 ◽  
Vol 113 (1) ◽  
pp. 142-155 ◽  
Author(s):  
A.B.J. Kuijlaars ◽  
S. Serra Capizzano
Keyword(s):  
Orthogonal Polynomials ◽  
Recurrence Coefficients ◽  
Zero Distribution ◽  
Asymptotic Zero Distribution

scholarly journals Asymptotic zero distribution of random orthogonal polynomials

2019 ◽  
Vol 47 (5) ◽  
pp. 3202-3230 ◽  
Author(s):  
Thomas Bloom ◽  
Duncan Dauvergne
Keyword(s):  
Orthogonal Polynomials ◽  
Zero Distribution ◽  
Asymptotic Zero Distribution

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.

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