- Title
- Characterization theorem for best linear spline approximation with free knots
- Creator
- Sukhorukova, Nadezda; Ugon, Julien
- Date
- 2010
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/36863
- Identifier
- vital:3802
- Identifier
- ISSN:1492-8760
- Abstract
- A necessary condition for a best Chebyshev approximation by piecewise linear functions is derived using quasidifferential calculus. We first discover some properties of the knots joining the linear functions. Then we use these properties to obtain the optimality condition. This condition is stronger than existing results. We present an example of linear spline approximation where the existing optimality conditions are satisfied, but not the proposed one, which shows that it is not optimal. Copyright © 2010 Watam Press.
- Relation
- Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms Vol. 17, no. 5 (2010), p. 687-708
- Rights
- Copyright Springer
- Rights
- This metadata is freely available under a CCO license
- Subject
- Chebyshev approximation; Linear splines; Quasidifferentials; Stationarity conditions
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