A Newton method for shape-preserving spline interpolation

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

Research output: Journal article publicationJournal articleAcademic researchpeer-review

12 Citations (Scopus)


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 languageEnglish
Pages (from-to)588-602
Number of pages15
JournalSIAM Journal on Optimization
Issue number2
Publication statusPublished - 1 Jan 2003


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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Software


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