scholarly journals On some Sobolev spaces with matrix weights and classical type Sobolev orthogonal polynomials

2021 ◽  
Vol 27 (2) ◽  
pp. 261-283
Author(s):  
S. M. Zagorodnyuk
Keyword(s):  
Orthogonal Polynomials ◽  
Sobolev Spaces ◽  
Classical Type ◽  
Matrix Weights ◽  
Sobolev Orthogonal Polynomials

scholarly journals Generalized Weighted Sobolev Spaces and Applications to Sobolev Orthogonal Polynomials I

2004 ◽  
Vol 80 (3) ◽  
pp. 273-308 ◽  
Author(s):  
José M. Rodríguez ◽  
Venancio Álvarez ◽  
Elena Romera ◽  
Domingo Pestana
Keyword(s):  
Orthogonal Polynomials ◽  
Sobolev Spaces ◽  
Weighted Sobolev Spaces ◽  
Sobolev Orthogonal Polynomials

scholarly journals Asymptotics for Jacobi–Sobolev orthogonal polynomials associated with non-coherent pairs of measures

2010 ◽  
Vol 162 (11) ◽  
pp. 1945-1963 ◽  
Author(s):  
Eliana X.L. de Andrade ◽  
Cleonice F. Bracciali ◽  
Laura Castaño-García ◽  
Juan J. Moreno-Balcázar
Keyword(s):  
Orthogonal Polynomials ◽  
Sobolev Orthogonal Polynomials ◽  
Coherent Pairs

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 General Sobolev Orthogonal Polynomials

1996 ◽  
Vol 200 (3) ◽  
pp. 614-634 ◽  
Author(s):  
Francisco Marcellán ◽  
Teresa E. Pérez ◽  
Miguel A. Piñar ◽  
André Ronveaux
Keyword(s):  
Orthogonal Polynomials ◽  
Sobolev Orthogonal Polynomials
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