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
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
2002
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), .
(doi:10.1137/S1052623401393128).
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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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
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Date deposited: 12 May 2006
Last modified: 16 Mar 2024 03:41
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Contributors
Author:
Asen L Dontchev
Author:
Liqun Qi
Author:
Hongxia Yin
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