Geometric dual formulation for first-derivative-based univariate cubic L-1 splines

doi:10.1007/s10898-006-9124-y

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	Geometric dual formulation for first-derivative-based univariate cubic L-1 splines
	Zhao, Y. B.2; Fang, S. -C.1,3; Lavery, J. E.4
	2008-04-01
发表期刊	JOURNAL OF GLOBAL OPTIMIZATION
ISSN	0925-5001
卷号	40 期号:4 页码:589-621
摘要	With the objective of generating "shape-preserving" smooth interpolating curves that represent data with abrupt changes in magnitude and/or knot spacing, we study a class of first-derivative-based C-1-smooth univariate cubic L-1 splines. An L-1 spline minimizes the L-1 norm of the difference between the first-order derivative of the spline and the local divided difference of the data. Calculating the coefficients of an L-1 spline is a nonsmooth non-linear convex program. Via Fenchel's conjugate transformation, the geometric dual program is a smooth convex program with a linear objective function and convex cubic constraints. The dual-to-primal transformation is accomplished by solving a linear program.
关键词	conjugate function convex program cubic L-1 spline shape-preserving interpolation piecewise polynomial
DOI	10.1007/s10898-006-9124-y
语种	英语
WOS研究方向	Operations Research & Management Science ; Mathematics
WOS类目	Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000253528100006
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/6669
专题	中国科学院数学与系统科学研究院
通讯作者	Fang, S. -C.
作者单位	1.N Carolina State Univ, Raleigh, NC 27695 USA 2.Chinese Acad Sci, Inst Appl Math, AMSS, Beijing 100080, Peoples R China 3.Tsinghua Univ, Dept Math Sci & Ind Engn, Beijing 100084, Peoples R China 4.USA, Res Off, Res Lab, Div Math, Res Triangle Pk, NC 27709 USA
推荐引用方式 GB/T 7714	Zhao, Y. B.,Fang, S. -C.,Lavery, J. E.. Geometric dual formulation for first-derivative-based univariate cubic L-1 splines[J]. JOURNAL OF GLOBAL OPTIMIZATION,2008,40(4):589-621.
APA	Zhao, Y. B.,Fang, S. -C.,&Lavery, J. E..(2008).Geometric dual formulation for first-derivative-based univariate cubic L-1 splines.JOURNAL OF GLOBAL OPTIMIZATION,40(4),589-621.
MLA	Zhao, Y. B.,et al."Geometric dual formulation for first-derivative-based univariate cubic L-1 splines".JOURNAL OF GLOBAL OPTIMIZATION 40.4(2008):589-621.