Title
The numerical solution of linear first kind Fredholm integral equations using an iterative method
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
Copyright Date
1987
Language
en
Proquest ID
AAI8721931
File Format
application/pdf
File Size
105 pages
Recommended Citation
Schmidt, Robert Craig, "The numerical solution of linear first kind Fredholm integral equations using an iterative method " (1987). Retrospective Theses and Dissertations. 8590.
https://lib.dr.iastate.edu/rtd/8590
