کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4643420 | 1341380 | 2006 | 18 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Multivariate approximation by a combination of modified Taylor polynomials
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We study an approximation of a multivariate function f by an operator of the form âi=1NTËr[f,xi](x)Ïi(x), where Ï1,â¦,ÏN are certain basis functions and TËr[f,xi](x) are modified Taylor polynomials of degree r expanded at xi. The modification is such that the operator has highest degree of algebraic precision. In the univariate case, this operator was investigated by Xuli [Multi-node higher order expansions of a function, J. Approx. Theory 124 (2003) 242-253]. Special attention is given to the case where the basis functions are a partition of unity of linear precision. For this setting, we establish two types of sharp error estimates. In the two-dimensional case, we show that this operator gives access to certain classical interpolation operators of the finite element method. In the case where Ï1,â¦,ÏN are multivariate Bernstein polynomials, we establish an asymptotic representation for the error as Nââ.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 196, Issue 1, 1 November 2006, Pages 162-179
Journal: Journal of Computational and Applied Mathematics - Volume 196, Issue 1, 1 November 2006, Pages 162-179
نویسندگان
Allal Guessab, Otheman Nouisser, Gerhard Schmeisser,