کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
513039 866445 2010 8 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the increasingly flat radial basis function and optimal shape parameter for the solution of elliptic PDEs
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
On the increasingly flat radial basis function and optimal shape parameter for the solution of elliptic PDEs
چکیده انگلیسی

For the interpolation of continuous functions and the solution of partial differential equation (PDE) by radial basis function (RBF) collocation, it has been observed that solution becomes increasingly more accurate as the shape of the RBF is flattened by the adjustment of a shape parameter. In the case of interpolation of continuous functions, it has been proven that in the limit of increasingly flat RBF, the interpolant reduces to Lagrangian polynomials. Does this limiting behavior implies that RBFs can perform no better than Lagrangian polynomials in the interpolation of a function, as well as in the solution of PDE? In this paper, arbitrary precision computation is used to test these and other conjectures. It is found that RBF in fact performs better than polynomials, as the optimal shape parameter exists not in the limit, but at a finite value.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Engineering Analysis with Boundary Elements - Volume 34, Issue 9, September 2010, Pages 802–809
نویسندگان
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