Maximal Order of Multipoint Iterations Using n Evaluations.
Abstract
This paper deals with multipoint iterations without memory for the solution of the nonlinear scalar equation f(m) (x) = 0, m > or = p sub n(m) be the maximal order of iterations which use n evaluations of the function or its derivatives per stop. We prove the Kung and Traub conjecture p sub n(m) (0) = 2(n-1) for Hermitian information. We show p sub n(m + 1) > or = p sub n(m) and conjecture p sub n(m) = 2(n-1). The problem of the maximal order is connected with Birkhoff interpolation. Under a certain assumption we prove that the Polya conditions are necessary for maximal order.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1975
- Accession Number
- ADA013604
Entities
People
- H. Wozniakowski
Organizations
- Carnegie Mellon University