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 |
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Pages (from-to) | 588-602 |
Number of pages | 15 |
Journal | SIAM Journal on Optimization |
Volume | 13 |
Issue number | 2 |
DOIs | |
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