On a bivariate interpolation problem

JOURNAL OF APPROXIMATION THEORY

卷:116

Article

Hakopian, HA ; Ismail, SAM

关键词: bivariate;    polynomial;    interpolation;    radial derivatives;    Birkhoff interpolation;    cubature formula;   

DOI  :  10.1006/jath.2001.3667

来源: Elsevier

【 摘 要 】

In this paper we solve the poisedness problem for a bivariate interpolation introduced by B. Bojanov and Y. Xu. The authors were informed the problem was solved earlier, by a different method, also by B. Bojanov and Y. Xu (to appear, On a Hermite interpolation by polynomials of two variables, SIAM J. Numer. Anal.). Parameters of the original interpolation from H., are the values of a function and its radial derivatives up to some order k at 2k + 1 equidistant nodes of the unit circumference. We also consider other closely related polynomial interpolations and prove their poisedness. Meanwhile the poisedness of several general univariate Birkhoff interpolation problems is proved to which the above problem is reduced. At the end we consider the corresponding useful cubature formulas. (C) 2002 Elsevier Science (USA).

【 授权许可】

Free