Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4607457 | Journal of Approximation Theory | 2012 | 5 Pages |
Abstract
For kâ{1,2,3,â¦}, we construct an even compactly supported piecewise polynomial Ïk whose Fourier transform satisfies Ak(1+Ï2)âkâ¤ÏÌk(Ï)â¤Bk(1+Ï2)âk, ÏâR, for some constants Bkâ¥Ak>0. The degree of Ïk is shown to be minimal, and is strictly less than that of Wendland's function Ï1,kâ1 when k>2. This shows that, for k>2, Wendland's piecewise polynomial Ï1,kâ1 is not of minimal degree if one places no restrictions on the number of pieces.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Amal Al-Rashdan, Michael J. Johnson,