New Numerical Methods. No Precedents

This book provides new high-order root approximating methods based on a general and unifying arithmetical concept: The Rational mean, encompassing the re-known Daniel Bernoulli´s, Newton´s, Halley´s and Householder´s root-solving algorithms, among many new others. The new methods do not require neither the use of derivatives nor any other concept related to infinitesimal calculus, but just the Simplest Arithmetic, any convergence rate can be achieved with ease.