Degree Type

Dissertation

Date of Award

1986

Degree Name

Doctor of Philosophy

Department

Mathematics

Abstract

The L(,(INFIN))-norm has been widely studied as a criterion of curve fitting problems. We are interested in the best L(,(INFIN))-approximation to a given finite array of number A = (a(,ij))(,mXn), i.e.;A natural iterated polishing (Mid-Range Polish) algorithm is shown, and its convergence in the L(,(INFIN))-norm is proved. Since the conver- gence of the Mid-Range Polish algorithm may take infinitely many iterations, we developed a new algorithm which converges in a finite number of steps to an optimal matrix of residual A* = (a(,ij)-r(,i)*-s(,j)*)(,mXn), whose L(,(INFIN))-norm u is the minimum one.;Several conditions are obtained, each of which is necessary and sufficient for a given matrix of residual to be optimal. For instance, a matrix of residual is optimal if and only if the set of entries, which equal to the L(,(INFIN))-norm of the matrix u in absolute value, contain a loop L alternating the value of u and -u. This criterion leads to an elegant and efficient finite algorithm for calculating the best L(,(INFIN))-approximation. Examples and results of the computational experience with a computer code version of some of the algorithms are presented.

DOI

https://doi.org/10.31274/rtd-180813-5770

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

Copyright Owner

Elsayed A. M. Eltelt

Language

en

Proquest ID

AAI8627106

File Format

application/pdf

File Size

136 pages

Included in

Mathematics Commons

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