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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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.
|Subjects:||Q Science > QA Mathematics|
|Divisions:||University Structure - Pre August 2011 > School of Mathematics > Operational Research
|Date Deposited:||11 May 2006|
|Last Modified:||06 Jun 2013 01:06|
|Contributors:||Dontchev, Asen L. (Author)
Qi, Houduo (Author)
Qi, Liqun (Author)
|Contact Email Address:||L.Qi@unsw.edu.au|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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