The numerical solution of linear first kind Fredholm integral equations using an iterative method

摘要

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.