Date of Award
Doctor of Philosophy
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.
Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/
Robert Craig Schmidt
Schmidt, Robert Craig, "The numerical solution of linear first kind Fredholm integral equations using an iterative method " (1987). Retrospective Theses and Dissertations. 8590.