On the exact degree of complexity of a class of operator equations of the second kind in a Hilbert space

Abstract

An exact complexity exponent is found for an approximate solution of a certain class of operator equations in a Hilbert space. A method for information setup and the algorithm realizing an optimal order are given. As a consequence, we find an exact complexity exponent for an approximate solution of Fredholm integral equations of second kind with kernels and free terms having square integrable ψ-derivatives.