Least-Square Iterative Techniques for Solving Integral Equations

摘要

Two iterative techniques for solving integral equations have been considered. The integrated square error is taken as the measure of deviation of the approximate solution from the exact solution. Starting with an arbitrary initial guess and a set of arbitrary chosen correction functions a convergent iteration scheme can be developed. Two special choices for the correction functions are considered: (1) the steepest-descent method; we choose the correction function as the function providing the steepest descent of the integrated square error; (2) the conjugate gradient method; we obtain an orthogonal set of the chosen correction functions (following from the steepest-descent method).