Explicit representations of changeable degree spline basis functions

Authors:
Wanqiang Shen;Guozhao Wang;Ping Yin
Affiliations:
School of Science, Jiangnan University, Wuxi, 214122, China and Department of Mathematics, Zhejiang University, Hangzhou, 310027, China;Department of Mathematics, Zhejiang University, Hangzhou, 310027, China;School of Science, Jiangnan University, Wuxi, 214122, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

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Abstract

Changeable degree spline (CD-spline for short) basis functions, defined by an iterative integral method, are extensions of B-spline basis functions. A CD-spline basis function is a piecewise function made up of polynomials of different degrees. In this paper, we will give the explicit representations of CD-spline basis functions, from which the spanned linear space can be seen clearly. Our method is also feasible for the explicit representations of the other basis functions given in analogous integral ways.