Title: Simultaneous point estimates for Newton's method
Language: English
Authors: Batra, Prashant  
Keywords: Convergence theorems;Newton iteration;Point estimates;Polynomial roots;Practical conditions for convergence;Simultaneous methods
Issue Date: 1-Sep-2002
Source: BIT Numerical Mathematics 42 (3): 467-476 (2002-09-01)
Journal or Series Name: BIT 
Abstract (english): 
Beside the classical Kantorovich theory there exist convergence criteria for the Newton iteration which only involve data at one point, i.e. point estimates. Given a polynomial P, these conditions imply the point evaluation of n = deg(P) functions (from a certain Taylor expansion). Such sufficient conditions ensure quadratic convergence to a single zero and have been used by several authors in the design and analysis of robust, fast and efficient root-finding methods for polynomials. In this paper a sufficient condition for the simultaneous convergence of the one-dimensional Newton iteration for polynomials will be given. The new condition involves only n point evaluations of the Newton correction and the minimum mutual distance of approximations to ensure "simultaneous" quadratic convergence to the pairwise distinct n roots.
URI: http://hdl.handle.net/11420/8918
ISSN: 0006-3835
Institute: Zuverlässiges Rechnen E-19 
Document Type: Article
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