کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9509667 | 1632061 | 2005 | 23 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Positive interpolatory quadrature formulas and para-orthogonal polynomials
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
We establish a relation between quadrature formulas on the interval [-1,1] that approximate integrals of the form Jμ(F)=â«-11F(x)μ(x)dx and SzegÅ quadrature formulas on the unit circle that approximate integrals of the form IÏ(f)=â«-ÏÏf(eiθ)Ï(θ)dθ. The functions μ(x) and Ï(θ) are assumed to be weight functions on [-1,1] and [-Ï,Ï], respectively, and are related by Ï(θ)=μ(cosθ)|sinθ|. It is well known that the nodes of SzegÅ formulas are the zeros of the so-called para-orthogonal polynomials Bn(z,Ï)=Φn(z)+ÏΦn*(z), |Ï|=1, Φn(z) and Φn*(z), being the orthogonal and reciprocal polynomials, respectively, with respect to the weight function Ï(θ). Furthermore, for Ï=±1, we have recently obtained Gauss-type quadrature formulas on [-1,1] (see Bultheel et al. J. Comput. Appl. Math. 132(1) (2000) 1). In this paper, making use of the para-orthogonal polynomials with Ïâ ±1, a one-parameter family of interpolatory quadrature formulas with positive coefficients for Jμ(F) is obtained along with error expressions for analytic integrands. Finally, some illustrative numerical examples are also included.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 179, Issues 1â2, 1 July 2005, Pages 97-119
Journal: Journal of Computational and Applied Mathematics - Volume 179, Issues 1â2, 1 July 2005, Pages 97-119
نویسندگان
Adhemar Bultheel, Leyla Daruis, Pablo González-Vera,