The Unimodality of Initial B-Spline Approximations in Spline Fitting  

作　　者：Zhiguo Yong Hongmei Kang Zhouwang Yang Yi Gu 

机构地区：[1]School of Mathematical Sciences,Soochow University,No.1 Shizi Street,Suzhou 215006,People’s Republic of China [2]University of Science and Technology of China,No.96 Road Jinzhai,Hefei,Anhui,People’s Republic of China

出　　处：《Communications in Mathematics and Statistics》2022年第2期331-352,共22页数学与统计通讯（英文）

基　　金：supported by the National Natural Science Foundation of China(No.11801393);the Natural Science Foundation of Jiangsu Province(No.BK20180831).

摘　　要：Finding optimal knots is a challenging problem in spline fitting due to a lack of prior knowledge regarding optimal knots.The unimodality of initial B-spline approximations associated with given data is a promising characteristic of locating optimal knots and has been applied successfully.The initial B-spline approximations herein are required to approximate given data well enough and characterized by the unimodality if jumps from the highest-order derivatives of the approximations at some interior knots are local maxima.In this paper,we prove the unimodality of the initial B-spline approximations that are constructed under two assumptions:Data points are sampled uniformly and sufficiently from B-spline functions,and initial knots are chosen as the parameters of sampling points.Our work establishes the theoretical basis of the unimodality of initial B-spline approximations and pioneers the theoretical study of locating optimal knots.

关 键 词：Unimodality property JUMPS Spline fitting B-spline approximations Optimal knots 

分 类 号：O17[理学—数学]