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

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

Research output: Journal article publicationJournal articleAcademic researchpeer-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 languageEnglish
Pages (from-to)123-143
Number of pages21
JournalConstructive Approximation
Volume19
Issue number1
DOIs
Publication statusPublished - 2003

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis
  • Computational Mathematics

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