New Numerical Methods. The Rational Mean© All rights reserved under international Copyright Conventions. 2013.No part of this publication may be either transmitted, or reproduced or stored by any means or in any form, mechanical, electronic, recording, scanning, photocopying or otherwise, with out the prior written permission of the author Domingo Gomez Morin
A new general and unifying arithmetical concept: The Rational Mean, which allows to generate, among many other new algorithms, those celebrated Lucas’s, Bernoulli’s, Newton’s, Halley’s, Householder’s
rootapproximating methods which up to now were considered the exclusive achievement of Infinitesimal Calculus. No derivatives, no trialanderror checkings, no geometry, no cartesian system, but just Simplest Arithmetic. These new highorder methods also embrace complex
roots and the general algebraic equation, and from the solid evidence at hand, these arithmetical methods have no precedents in the mathematics literature. Indeed, it is really striking to realize that even ancient mathematicians had at hand the elementary tools for constructing these highorder algorithms. Actually, these new findings compel us to cogitate on the reasons mathematicians were forced to create the "elevated" infinitesimal system that we have inherited.
The book also includes the new Generalized Continued Fractions for approximating the maximum and the minimum modulus root of the general algebraic equation, number Pi, number e, Golden Mean, and others with improved convergence rate.
As an example follows page 44, with the matricial expression (S^{k} nxn) that compiles some of the new general arithmetical methods for approximating the nth root of a number P, with any desired convergence rate k (See also page 34 below):
Available only in electronic form: PDF file. Save the Planet. Please see some sample pages below. Language: English. 92 pages including frontcover and backcover. Latex typesetting. Electronic page format B5:182x257 mm. After using PayPal please email me and I'll immediately send the electronic book (PDF) to you.
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Follow few selected pages from the book with tidbits on the new methods:

