KMS Of Academy of mathematics and systems sciences, CAS
| 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 | |
| Source Publication | JOURNAL OF GLOBAL OPTIMIZATION
 |
| ISSN | 0925-5001 |
| Volume | 40Issue:4Pages:589-621 |
| Abstract | 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. |
| Keyword | conjugate function convex program cubic L-1 spline shape-preserving interpolation piecewise polynomial |
| DOI | 10.1007/s10898-006-9124-y |
| Language | 英语 |
| WOS Research Area | Operations Research & Management Science ; Mathematics |
| WOS Subject | Operations Research & Management Science ; Mathematics, Applied |
| WOS ID | WOS:000253528100006 |
| Publisher | SPRINGER |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/6669 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Fang, S. -C. |
| Affiliation | 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 |
| Recommended Citation 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. |
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