Quadratic convergence of Newton's method for convex interpolation and smoothing

A.L. Dontchev; H. Qi; Liqun Qi

doi:10.1007/s00365-002-0513-2

Quadratic convergence of Newton's method for convex interpolation and smoothing

A.L. Dontchev, H. Qi, Liqun Qi

Research output: Journal article publication › Journal article › Academic research › peer-review

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 [7] and strengthening a result of Andersson and Elfving [1] and our previous work [5]. 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.

Original language	English
Pages (from-to)	123-143
Number of pages	21
Journal	Constructive Approximation
Volume	19
Issue number	1
DOIs	https://doi.org/10.1007/s00365-002-0513-2
Publication status	Published - 2003

Keywords

Convex best interpolation
Convex smoothing
Splines
Newton's method
Quadratic convergence

ASJC Scopus subject areas

General Mathematics
Analysis
Computational Mathematics

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10.1007/s00365-002-0513-2

Cite this

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title = "Quadratic convergence of Newton's method for convex interpolation and smoothing",

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 [7] and strengthening a result of Andersson and Elfving [1] and our previous work [5]. 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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AU - Dontchev, A.L.

AU - Qi, H.

AU - Qi, Liqun

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N2 - 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 [7] and strengthening a result of Andersson and Elfving [1] and our previous work [5]. 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.

AB - 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 [7] and strengthening a result of Andersson and Elfving [1] and our previous work [5]. 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.

KW - Convex best interpolation

KW - Convex smoothing

KW - Splines

KW - Newton's method

KW - Quadratic convergence

U2 - 10.1007/s00365-002-0513-2

DO - 10.1007/s00365-002-0513-2

M3 - Journal article

SN - 0176-4276

VL - 19

SP - 123

EP - 143

JO - Constructive Approximation

JF - Constructive Approximation

IS - 1

ER -

Quadratic convergence of Newton's method for convex interpolation and smoothing

Abstract

Keywords

ASJC Scopus subject areas

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