A Newton method for shape-preserving spline interpolation

Asen L. Dontchev; Hou Duo Qi; Liqun Qi; Hongxia Yin

doi:10.1137/S1052623401393128

A Newton method for shape-preserving spline interpolation

Asen L. Dontchev
, Hou Duo Qi
, Liqun Qi
, Hongxia Yin

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

12 Citations (Scopus)

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.

Original language	English
Pages (from-to)	588-602
Number of pages	15
Journal	SIAM Journal on Optimization
Volume	13
Issue number	2
DOIs	https://doi.org/10.1137/S1052623401393128
Publication status	Published - 1 Jan 2003

Keywords

Newton's method
Quadratic convergence
Semismooth equation
Shape-preserving interpolation
Splines

ASJC Scopus subject areas

Theoretical Computer Science
Software

More information

10.1137/S1052623401393128

http://hdl.handle.net/10397/4760

Cite this

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title = "A Newton method for shape-preserving spline interpolation",

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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AU - Qi, Liqun

AU - Yin, Hongxia

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Y1 - 2003/1/1

N2 - 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.

AB - 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.

KW - Newton's method

KW - Quadratic convergence

KW - Semismooth equation

KW - Shape-preserving interpolation

KW - Splines

UR - https://www.scopus.com/pages/publications/0013103573

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DO - 10.1137/S1052623401393128

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A Newton method for shape-preserving spline interpolation

Abstract

Keywords

ASJC Scopus subject areas

More information

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