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Newton Raphson method, scaling at fractal boundaries and Mathematica

Technical Report:

Abstract

The basins of convergence of cubic polynomials having real roots are studied using Newton Raphson iterative method. The limiting value for the ratio of basin segments for equispaced roots is explained. An algorithm is presented for computing the basin boundaries on the real axis which obviates the necessity of taking recourse to extensive search. Mathematica programs have been developed to help in the above study and also to depict the basins in the complex plane. (author). 10 refs, 5 figs.
Publication Date:
Sep 01, 1994
Product Type:
Technical Report
Report Number:
IC-94/268
Reference Number:
SCA: 661100; PA: AIX-26:012159; EDB-95:031956; SN: 95001324636
Resource Relation:
Other Information: PBD: Sep 1994
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; POLYNOMIALS; CONVERGENCE; NEWTON METHOD; ALGORITHMS; FRACTALS; M CODES; 661100; CLASSICAL AND QUANTUM MECHANICS
OSTI ID:
10112375
Research Organizations:
International Centre for Theoretical Physics (ICTP), Trieste (Italy)
Country of Origin:
IAEA
Language:
English
Other Identifying Numbers:
Other: ON: DE95613374; TRN: XA9438433012159
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
INIS
Size:
19 p.
Announcement Date:
Jun 30, 2005

Technical Report:

Citation Formats

Bisoi, Ajay Kumar. Newton Raphson method, scaling at fractal boundaries and Mathematica. IAEA: N. p., 1994. Web.
Bisoi, Ajay Kumar. Newton Raphson method, scaling at fractal boundaries and Mathematica. IAEA.
Bisoi, Ajay Kumar. 1994. "Newton Raphson method, scaling at fractal boundaries and Mathematica." IAEA.
@misc{etde_10112375,
title = {Newton Raphson method, scaling at fractal boundaries and Mathematica}
author = {Bisoi, Ajay Kumar}
abstractNote = {The basins of convergence of cubic polynomials having real roots are studied using Newton Raphson iterative method. The limiting value for the ratio of basin segments for equispaced roots is explained. An algorithm is presented for computing the basin boundaries on the real axis which obviates the necessity of taking recourse to extensive search. Mathematica programs have been developed to help in the above study and also to depict the basins in the complex plane. (author). 10 refs, 5 figs.}
place = {IAEA}
year = {1994}
month = {Sep}
}