Error Bounds for Newton's Iterates Derived from the Kantorovich Theorem.
Abstract
In this paper, it is shown that the upper and lower bounds of the errors in the Newton iterates recently obtained by Potra-Ptak and Miel, with the use of nondiscrete induction and majorizing sequence, respectively, follow immediately from the Kantorovich theorem and the Kantorovich recurrence relations. It is also shown that the upper and lower bounds of Miel are sharper than those of Potra-Ptak. Keywords: Numerical analysis; Potra-Ptak's bounds; Miel's bounds.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1985
- Accession Number
- ADA160959
Entities
People
- Tetsuro Yamamoto
Organizations
- University of Wisconsin–Madison