One sided Hermite interpolation by piecewise different generalized polynomials
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摘要
Piecewise generalized polynomials of different kinds of order n (ECT-splines of order n) are constructed from different ECT-systems of order n via connection matrices which are nonsingular and totally positive.A well-known zero count for polynomial splines is extended to ECT-splines. It is used to construct ECT-B-splines and to show under which conditions ECT-splines will solve modified Hermite-type interpolation problems. Also conditions are specified such that piecewise generalized polynomials form rECT-systems and the interpolation problems associated with may be solved recursively.
论文关键词:41A15,41A05,ECT-systems,Generalized polynomials,Generalized piecewise polynomials,Modified Hermite interpolation,One sided Hermite interpolation
论文评审过程:Received 16 February 2005, Available online 7 November 2005.
论文官网地址:https://doi.org/10.1016/j.cam.2005.06.045