Iterative Methods for Best Approximate Solutions of Linear Integral Equations of the First and Second Kinds

摘要

Least squares solutions of Fredholm and Volterra equations of the first and second kinds are studied using generalized inverses. The method of successive approximations, the steepest descent and the conjugate gradient methods are shown to converge to a least squares solution or to a least squares solution of minimal norm, both for integral equations of the first and second kinds. An iterative method for matrices due to Cimmino is generalized to integral equations of the first kind and its convergence to the least squares solution of minimal norm is established. (Author)