Convergence Of The Iteration Process In The Solution Of Algebraic And Transcendental Equations
Date of Award
Master of Science
The science of algebra arose in an effort to solve equations. Since the main objects in algebra have been the discussion of equalities and the transformation of forms into simpler equivalent ones, that science may well be called the Science of Equations. The solution of an equation containing one unknown quantity consists of the determination of its value or values, these being called roots. An algebraic equation of degree n has n roots, while transcendental equations have an infinite number of roots. There has existed for years the problem of finding values, as exact as possible, or as close as one wishes of the roots. It is the object of the study to show the convergence of the iteration process and methods of inducing convergence in numerical analysis. The use of a computer in testing convergence of algebraic and transcendental equations is also shown.
The definitions of convergence and divergence are now commonplace in elementary analysis. The ideas were familiar to mathematicians before Newton and leibuix; and all the great mathematicians of the seventeenth and eighteen centuries.
Bo Definitions. The following terms and expressions will he used throughout this paper. Their definitions are given here.
Definition 1: Transcendental equation - An equation for which there is no general method of stating its roots in terms of its coefficients. (Example: a ex + b cos = + 0)
Definition 1.1: Iteration - The process of repeating to give successive approximations.
Definition 1.2: Convergence - lim Sn = U : Sn approaches the limit U. The value of the series is the number U (sometimes called the sum).
A. D. Stewart
Prairie View A&M College
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Date of Digitization
John B Coleman Library
City of Publication
Anderson, J. R. (1970). Convergence Of The Iteration Process In The Solution Of Algebraic And Transcendental Equations. Retrieved from https://digitalcommons.pvamu.edu/pvamu-theses/1487