Convergence of Newton's method for convex best interpolation
Dontchev, Asen L., Qi, Houduo and Qi, Liqun (2001) Convergence of Newton's method for convex best interpolation. Numerische Mathematik, 87, (3), 435-456. (doi:10.1007/PL00005419).
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Description/Abstract
In this paper, we consider the problem of finding a convex function which interpolates given points and has a minimal L2 norm of the second derivative. This problem reduces to a system of equations involving semismooth functions. We study a Newton-type method utilizing Clarke's generalized Jacobian and prove that its local convergence is superlinear. For a special choice of a matrix in the generalized Jacobian, we obtain the Newton method proposed by Irvine et al. and settle the question of its convergence. By using a line search strategy, we present a global extension of the Newton method considered. The efficiency of the proposed global strategy is confirmed with numerical experiments.
| Item Type: | Article |
|---|---|
| ISSNs: | 0029-599X (print) |
| Related URLs: | |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | University Structure - Pre August 2011 > School of Mathematics > Operational Research |
| Item ID: | 29638 |
| Date Deposited: | 11 May 2006 |
| Last Modified: | 06 Jun 2013 01:06 |
| Contributors: | Dontchev, Asen L. (Author) Qi, Houduo (Author) Qi, Liqun (Author) |
| Date: | January 2001 |
| Status: | Published |
| Contact Email Address: | L.Qi@unsw.edu.au |
| URI: | http://eprints.soton.ac.uk/id/eprint/29638 |
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