Regularized solution to the Fredholm integral equation of the first kind with noisy data

Abstract： In this paper, we use a regularization method to solve the Fredholm integral equation of the first kind. Under the assumption that measured data are contaminated with deterministic errors whose root mean square value is bounded by a noise level, we obtain two error estimates. The convergence rates can be obtained under the suitable choices of regularization parameters and the number of measured points. Some numerical experiments show that the proposed method is effective and accurate.