کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4615498 | 1339318 | 2015 | 17 صفحه PDF | دانلود رایگان |
We introduce a family of piecewise-exponential functions that have the Hermite interpolation property. Our design is motivated by the search for an effective scheme for the joint interpolation of points and associated tangents on a curve with the ability to perfectly reproduce ellipses. We prove that the proposed Hermite functions form a Riesz basis and that they reproduce prescribed exponential polynomials. We present a method based on Green's functions to unravel their multi-resolution and approximation-theoretic properties. Finally, we derive the corresponding vector and scalar subdivision schemes, which lend themselves to a fast implementation. The proposed vector scheme is interpolatory and level-dependent, but its asymptotic behavior is the same as the classical cubic Hermite spline algorithm. The same convergence properties—i.e., fourth order of approximation—are hence ensured.
Journal: Journal of Mathematical Analysis and Applications - Volume 426, Issue 1, 1 June 2015, Pages 211–227