Aspects of numerical analysis relative to computing

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
James Douglas Arthur (Creator)
The University of North Carolina at Greensboro (UNCG )
Web Site:
Hughes Hoyle

Abstract: The purpose of this thesis is to investigate the problem of finding zeros of various functions through iterative methods. Chapter One is concerned with deriving an iterative function in such a manner as to insure that its fixed point is a zero of the function with which we started. The relevance of the Lipschitz Condition is unveiled as criteria are hypothesized and proven to insure the existence of the fixed point property. After certain conditions have been formulated, Chapter One then deals with the actual derivation of an iterative function. It also specifies under what conditions convergence to a fixed point can be accelerated. Chapter Two then takes the concepts of Chapter One, incorporates them into a computer program and illustrates what has been previously proven. Two different iterative methods were applied to the same function and then accelerated processes were used on them. While Chapter One deals with the derivation of an iterative function and guaranteeing its convergence once the iteration process has started, Chapter Three theorizes a method to give an initial starting value for the process. Thus, Chapter Three deals with Bernoulli's Method and the conditions which must be imposed to insure the proper starting value.

Additional Information

Language: English
Date: 1973
Numerical analysis $x Computer programs
Iterative methods (Mathematics)

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