Multi-projection methods for Fredholm integral equations of the first kind

Abstract

We use piecewise polynomial basis functions to obtain the stable approximation solution of the Tikhonov regularized equation of the Fredholm integral equation of the first kind by utilizing multi-projection (multi-Galerkin and multi-collocation) methods. We evaluate the error bounds for the approximate solution with the exact solution in infinity norm. We provide an a priori parameter choice strategy under infinity norm. In addition to determining the regularization parameter, we discuss Arcangeli's discrepancy principle and calculate the convergence rates in infinity norm. We give test examples to validate the theoretical results.