Validation and verification of a third degree optimization method

by Levin, Anders; Johannesson, Jörgen

Abstract (Summary)
This combined master thesis in Mathematics and in Computer Science deals with a method for finding the local minimum of a unimodal function inside a given interval by using a fifth degree polynomial. This fifth degree polynomial is created from the function value and the first and second derivative values in the end-points of the interval. In this report the presented method is derived mathematically to converge and it is then proven that the method has a convergence rate of three. Last is the method tested against two reference methods to see the usefullness of the method. To do this some software development methods are described in the report and some test strategies are given. The tests are done with six different functions and with three different implementations of the method. The conclusions from the tests are that it is often better to use one of the referencemethods instead of the presented method, even if the presented method has a better convergence rate, and that the method needs to handle when the found approximation always is on one side of the interval. We could also see from the tests that none of the methods were good on finding a correct approximation. Therefore, there exist needs for more secure methods. It is therefore suggested in the report that a search for other interpolating functions ought to be carried out in order to improve the method. Also, it could be interesting to test against another method with even higher convergence rate. To do that, another numerical representation is needed and it would be interesting to see if that changes the outcome
Bibliographical Information:


School:Växjö universitet

School Location:Sweden

Source Type:Master's Thesis

Keywords:optimization convergence rate software development


Date of Publication:05/03/2005

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