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A Newton method for shape-preserving spline interpolation

A Newton method for shape-preserving spline interpolation
A Newton method for shape-preserving spline interpolation
In 1986, Irvine, Marin, and Smith proposed a Newton-type method for shape-preserving interpolation and, based on numerical experience, conjectured its quadratic convergence. In this paper, we prove local quadratic convergence of their method by viewing it as a semismooth Newton method. We also present a modification of the method which has global quadratic convergence. Numerical examples illustrate the results.
shape-preserving interpolation, splines, semismooth equation, Newton's method, quadratic convergence
1052-6234
588-602
Dontchev, Asen L
7c78300a-aef9-441f-9932-ac36f723d809
Qi, Hou-Duo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Qi, Liqun
69936be7-f1aa-4c1f-b403-5bd5f3ba7d4c
Yin, Hongxia
737823b3-a3a8-4d92-bb15-19b9b58a7adf
Dontchev, Asen L
7c78300a-aef9-441f-9932-ac36f723d809
Qi, Hou-Duo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Qi, Liqun
69936be7-f1aa-4c1f-b403-5bd5f3ba7d4c
Yin, Hongxia
737823b3-a3a8-4d92-bb15-19b9b58a7adf

Dontchev, Asen L, Qi, Hou-Duo, Qi, Liqun and Yin, Hongxia (2002) A Newton method for shape-preserving spline interpolation. SIAM Journal on Optimization, 13 (2), 588-602. (doi:10.1137/S1052623401393128).

Record type: Article

Abstract

In 1986, Irvine, Marin, and Smith proposed a Newton-type method for shape-preserving interpolation and, based on numerical experience, conjectured its quadratic convergence. In this paper, we prove local quadratic convergence of their method by viewing it as a semismooth Newton method. We also present a modification of the method which has global quadratic convergence. Numerical examples illustrate the results.

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More information

Published date: 2002
Keywords: shape-preserving interpolation, splines, semismooth equation, Newton's method, quadratic convergence
Organisations: Operational Research

Identifiers

Local EPrints ID: 29640
URI: http://eprints.soton.ac.uk/id/eprint/29640
ISSN: 1052-6234
PURE UUID: ee442caf-8242-4267-9b1a-60a1a82c9a24
ORCID for Hou-Duo Qi: ORCID iD orcid.org/0000-0003-3481-4814

Catalogue record

Date deposited: 12 May 2006
Last modified: 20 Jul 2019 00:57

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