Degree Type
Dissertation
Date of Award
1981
Degree Name
Doctor of Philosophy
Department
Mathematics
Abstract
A convergence theorem for Lee and Prenter's filtered leastsquares method for solving the Fredholm first kind equationKf = g is corrected. Under suitable restrictions, the filtered least squares method is shown to be well-posed under compact perturbations in K and arbitrary perturbations in g;The M-solution of the Fredholm first kind equation Kf = g is the unique minimum norm element f (epsilon) M which minimizes (VBAR)(VBAR)Kf - g(VBAR)(VBAR), where M is a finite dimensional subspace of the given Hilbert space. Several convergence results are proved for the M-solution. A modified Gram-Schmidt method for calculating the M-solution of Kf = g is compared to a modification of the normal equations method which is used to calculate the M-solution of Kf = g. This modified Gram-Schmidt method is shown to be well-posed under compact perturbations in K and arbitrary perturbations in g;A convergence theorem for Marti's method for solving the Fredholm first kind equation Kf = g is corrected. Marti's method is shown to be well-posed under perturbations in g. It is shown that Marti's method is not necessarily well-posed under compact perturbations in K. Also included are results relating Marti's solution to the M-solution of Kf = g and to the least square solution of minimum norm of Kf = g;References;Lee, J. W; and Prenter, P. M. "An Analysis of the Numerical Solution of Fredholm Integral Equations of the First Kind." Numerische Mathematik 30 (1978):1-23;Marti, J. T. "An Algorithm for Computing Minimum Norm Solutions of Fredholm Integral Equations of the First Kind." SIAM Journal of Numerical Analysis 15 (December 1978):1071-1076.
DOI
https://doi.org/10.31274/rtd-180813-6181
Publisher
Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/
Copyright Owner
Kevin Ray Hickey
Copyright Date
1981
Language
en
Proquest ID
AAI8122522
File Format
application/pdf
File Size
135 pages
Recommended Citation
Hickey, Kevin Ray, "The numerical solution of Fredholm integral equations of the first kind " (1981). Retrospective Theses and Dissertations. 7175.
https://lib.dr.iastate.edu/rtd/7175
