Univariate cubic L 1 splines – A geometric programming approach

Hao Cheng, Shu-Cherng Fang and John E. Lavery

Mathematical Methods of Operations Research, 2002, vol. 56, issue 2, 197-229

Abstract: Univariate cubic L 1 splines provide C 1 -smooth, shape-preserving interpolation of arbitrary data, including data with abrupt changes in spacing and magnitude. The minimization principle for univariate cubic L 1 splines results in a nondifferentiable convex optimization problem. In order to provide theoretical treatment and to develop efficient algorithms, this problem is reformulated as a generalized geometric programming problem. A geometric dual with a linear objective function and convex quadratic constraints is derived. A linear system for dual to primal conversion is established. The results of computational experiments are presented. In the natural norm for this class of problems, namely, the L 1 norm of the second derivative, the geometric programming approach finds better solutions than the previously used discretization method. Copyright Springer-Verlag Berlin Heidelberg 2002

Keywords: Key words: cubic L1 spline; geometric programming; interpolation; spline function; univariate (search for similar items in EconPapers)
Date: 2002
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://hdl.handle.net/10.1007/s001860200216 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:mathme:v:56:y:2002:i:2:p:197-229

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/00186

DOI: 10.1007/s001860200216

Access Statistics for this article

Mathematical Methods of Operations Research is currently edited by Oliver Stein

More articles in Mathematical Methods of Operations Research from Springer, Gesellschaft für Operations Research (GOR), Nederlands Genootschap voor Besliskunde (NGB)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().