# Ostrowski-Like Method with Corrections for the Inclusion of Polynomial Zeros

Ostrowski-Like Method with Corrections for the Inclusion of Polynomial Zeros In this paper we construct iterative methods of Ostrowski's type for the simultaneous inclusion of all zeros of a polynomial. Using the concept of the R-order of convergence of mutually dependent sequences, we present the convergence analysis of the total-step and the single-step methods with Newton and Halley's corrections. The case of multiple zeros is also considered. The suggested algorithms possess a great computational efficiency since the increase of the convergence rate is attained without additional calculations. Numerical examples and an analysis of computational efficiency are given. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

# Ostrowski-Like Method with Corrections for the Inclusion of Polynomial Zeros

, Volume 10 (6) – Nov 19, 2004
31 pages

/lp/springer_journal/ostrowski-like-method-with-corrections-for-the-inclusion-of-polynomial-mw9Jvt2tgH
Publisher
Springer Journals
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/B:REOM.0000047094.39609.f6
Publisher site
See Article on Publisher Site

### Abstract

In this paper we construct iterative methods of Ostrowski's type for the simultaneous inclusion of all zeros of a polynomial. Using the concept of the R-order of convergence of mutually dependent sequences, we present the convergence analysis of the total-step and the single-step methods with Newton and Halley's corrections. The case of multiple zeros is also considered. The suggested algorithms possess a great computational efficiency since the increase of the convergence rate is attained without additional calculations. Numerical examples and an analysis of computational efficiency are given.

### Journal

Reliable ComputingSpringer Journals

Published: Nov 19, 2004

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