Quadratic convergence of Newton's method for convex interpolation and smoothing
Quadratic convergence of Newton's method for convex interpolation and smoothing
In this paper, we prove that Newton's method for convex best interpolation is locally quadratically convergent, giving an answer to a question of Irvine, Marin, and Smith and strengthening a result of Andersson and Elfving and our previous work. A damped Newton-type method is presented which has global quadratic convergence. Analogous results are obtained for the convex smoothing problem. Numerical examples are presented.
convex best interpolation, convex smoothing, splines, newton's method, quadratic convergence
123-143
Dontchev, A.L.
080775ad-90b3-482d-95bd-a6dbfedaab9d
Qi, H.
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Qi, L.
d1312bc6-c7fc-45e0-b75d-baaf78babbc1
2003
Dontchev, A.L.
080775ad-90b3-482d-95bd-a6dbfedaab9d
Qi, H.
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Qi, L.
d1312bc6-c7fc-45e0-b75d-baaf78babbc1
Dontchev, A.L., Qi, H. and Qi, L.
(2003)
Quadratic convergence of Newton's method for convex interpolation and smoothing.
Constructive Approximation, 19 (1), .
(doi:10.1007/s00365-002-0513-2).
Abstract
In this paper, we prove that Newton's method for convex best interpolation is locally quadratically convergent, giving an answer to a question of Irvine, Marin, and Smith and strengthening a result of Andersson and Elfving and our previous work. A damped Newton-type method is presented which has global quadratic convergence. Analogous results are obtained for the convex smoothing problem. Numerical examples are presented.
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Published date: 2003
Keywords:
convex best interpolation, convex smoothing, splines, newton's method, quadratic convergence
Organisations:
Operational Research
Identifiers
Local EPrints ID: 29644
URI: http://eprints.soton.ac.uk/id/eprint/29644
ISSN: 0176-4276
PURE UUID: dbbfde6f-cb92-4c2b-96ec-a21a7e2acc43
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Date deposited: 12 May 2006
Last modified: 16 Mar 2024 03:41
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Author:
A.L. Dontchev
Author:
L. Qi
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