THE FINITE-SECTION APPROXIMATION
FOR ILL-POSED INTEGRAL EQUATIONS
ON THE HALF-LINE

SERGEI PEREVERZEV AND EBERHARD SCHOCK

Abstract:

Integral equations on the half-line are commonly approximated by the finite-section approximation, in which the infinite upper limit is replaced by a positive number called the finite-section parameter. In this paper we consider the finite-section approximation for the first kind integral equations, which are typically ill-posed and call for regularization. For some classes of such equations corresponding to inverse problems from optics and astronomy, we indicate the finite-section parameters that allow us to apply standard regularization techniques. Two discretization schemes for the finite-section equations are also proposed and their efficiency is studied.