Strong Stieltjes distributions and orthogonal Laurent polynomials with applications to quadratures and Padé approximation
نویسندگان
چکیده
Starting from a strong Stieltjes distribution φ, general sequences of orthogonal Laurent polynomials are introduced and some of their most relevant algebraic properties are studied. From this perspective, the connection between certain quadrature formulas associated with the distribution φ and two-point Padé approximants to the Stieltjes transform of φ is revisited. Finally, illustrative numerical examples are discussed.
منابع مشابه
Orthogonal Laurent polynomials corresponding to certain strong Stieltjes distributions with applications to numerical quadratures
In this paper we shall be mainly concerned with sequences of orthogonal Laurent polynomials associated with a class of strong Stieltjes distributions introduced by A.S. Ranga. Algebraic properties of certain quadratures formulae exactly integrating Laurent polynomials along with an application to estimate weighted integrals on [−1, 1] with nearby singularities are given. Finally, numerical exam...
متن کاملConvergence of Padé approximants of Stieltjes-type meromorphic functions and the relative asymptotics of orthogonal polynomials on the real line
We obtain results on the convergence of Padé approximants of Stieltjes-type meromorphic functions and the relative asymptotics of orthogonal polynomials on unbounded intervals. These theorems extend some results given by Guillermo López in this direction substituting the Carleman condition in his theorems by the determination of the corresponding moment problem. c © 2009 Elsevier Inc. All right...
متن کاملOrthogonal rational functions and quadrature on the real half line
In this paper we generalize the notion of orthogonal Laurent polynomials to orthogonal rational functions. Orthogonality is considered with respect to a measure on the positive real line. From this, Gauss-type quadrature formulas are derived and multipoint Padé approximants for the Stieltjes transform of the measure. Convergence of both the quadrature formula and the multipoint Padé approximant...
متن کاملForeword to the proceedings of the OrthoQuad 2014 conference
OrthoQuad 2014 was an international symposium on orthogonality, quadrature, and related topics, held on January 20-24, 2014 in Puerto de la Cruz, Tenerife, Spain. It was held in memory of Professor Pablo González-Vera (1955-2012). 1. A short CV of Pablo González-Vera Pablo González-Vera was born in Vallehermoso (La Gomera, Canary Islands) on January 25, 1955. He studied Mathematics at Universit...
متن کاملSolving singular integral equations by using orthogonal polynomials
In this paper, a special technique is studied by using the orthogonal Chebyshev polynomials to get approximate solutions for singular and hyper-singular integral equations of the first kind. A singular integral equation is converted to a system of algebraic equations based on using special properties of Chebyshev series. The error bounds are also stated for the regular part of approximate solut...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Math. Comput.
دوره 74 شماره
صفحات -
تاریخ انتشار 2005