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Titolo:
Convergence of Newton's method for convex best interpolation
Autore:
Dontchev, AL; Qi, HD; Qi, LQ;
Indirizzi:
Math Reviews, Ann Arbor, MI 48107 USA Math Reviews Ann Arbor MI USA 48107Math Reviews, Ann Arbor, MI 48107 USA Univ New S Wales, Sch Math, Sydney, NSW 2052, Australia Univ New S Wales Sydney NSW Australia 2052 h, Sydney, NSW 2052, Australia
Titolo Testata:
NUMERISCHE MATHEMATIK
fascicolo: 3, volume: 87, anno: 2001,
pagine: 435 - 456
SICI:
0029-599X(200101)87:3<435:CONMFC>2.0.ZU;2-1
Fonte:
ISI
Lingua:
ENG
Soggetto:
NONLINEAR COMPLEMENTARITY-PROBLEMS; HILBERT-SPACE; CONSTRAINED INTERPOLATION; CUBIC-SPLINES; APPROXIMATION; ALGORITHM; EQUATIONS; DUALITY; SUBSET;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Citazioni:
31
Recensione:
Indirizzi per estratti:
Indirizzo: Dontchev, AL Math Reviews, Ann Arbor, MI 48107 USA Math Reviews Ann ArborMI USA 48107 Ann Arbor, MI 48107 USA
Citazione:
A.L. Dontchev et al., "Convergence of Newton's method for convex best interpolation", NUMER MATH, 87(3), 2001, pp. 435-456

Abstract

In this paper, we consider the problem of finding a convex function which interpolates given points and has a minimal L-2 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 choiceof a matrix in the generalized Jacobian, we obtain the Newton method proposed by Irvine et al. [17] 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 confirmedwith numerical experiments.

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Documento generato il 04/04/20 alle ore 09:13:37