KNOT PLACEMENT FOR B-SPLINE CURVE APPROXIMATION VIA l_(∞,1)-NORM AND DIFFERENTIAL EVOLUTION ALGORITHM  

作　　者：Jiaqi Luo Hongmei Kang Zhouwang Yang 

机构地区：[1]School of Mathematical Sciences,Soochow University,Suzhou 215008,China [2]School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China

出　　处：《Journal of Computational Mathematics》2022年第4期589-606,共18页计算数学（英文）

基　　金：supported by the National Natural Science Foundation of China(Nos.11871447,11801393);the Natural Science Foundation of Jiangsu Province(No.BK20180831).

摘　　要：In this paper,we consider the knot placement problem in B-spline curve approximation.A novel two-stage framework is proposed for addressing this problem.In the first step,the l_(∞,1)-norm model is introduced for the sparse selection of candidate knots from an initial knot vector.By this step,the knot number is determined.In the second step,knot positions are formulated into a nonlinear optimization problem and optimized by a global optimization algorithm—the differential evolution algorithm(DE).The candidate knots selected in the first step are served for initial values of the DE algorithm.Since the candidate knots provide a good guess of knot positions,the DE algorithm can quickly converge.One advantage of the proposed algorithm is that the knot number and knot positions are determined automatically.Compared with the current existing algorithms,the proposed algorithm finds approximations with smaller fitting error when the knot number is fixed in advance.Furthermore,the proposed algorithm is robust to noisy data and can handle with few data points.We illustrate with some examples and applications.

关 键 词：B-spline curve approximation Knot placement l_(∞ 1)-norm Differential Evolution algorithm 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]