|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|
|Appears in Collections:||Publications without fulltext|
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