Degree Type

Dissertation

Date of Award

1987

Degree Name

Doctor of Philosophy

Department

Mathematics

Abstract

In 1974, O. N. Strand proposed solving the first kind equation Kf = g using an iterative method of the form f[subscript]n = f[subscript]n-1 + DK*(g - Kf[subscript] n-1), n = 1, 2, ..., where D is an appropriately chosen linear operator. This method was modified in 1978 by J. Graves and P. Prenter for the case when K is a Hermitian operator. The Strand method is generalized in this paper to the form f[subscript]n = f[subscript]n-1 + D[subscript]nK*(g - Kf[subscript] n-1), n = 1, 2, ..., where each D[subscript]n is an appropriate linear operator. A corresponding generalization for the Graves and Prenter method is also given. A technique for choosing the operators D[subscript]n, n = 1, 2, ... is given. This technique results in an iteration which converges two to three times faster than the corresponding Strand or Graves and Prenter iteration. Numerical examples illustrating this accelerated convergence are given.

DOI

https://doi.org/10.31274/rtd-180813-11456

Publisher

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

Copyright Owner

Robert Craig Schmidt

Language

en

Proquest ID

AAI8721931

File Format

application/pdf

File Size

105 pages

Included in

Mathematics Commons

Share

COinS