Iterative solution methods for ill-posed problems

We describe new iterative methods for the solution of large ill-conditioned that arise from the discretization of ill-posed problems. In these methods a filter function, which determines the regularization of the problem, is chosen and expanded in terms of orthogonal polynomials. Each iteration yields one new term in this expansion. A variety of iterative methods, which differ in the choice of filter function and orthogonal polynomials, can be derived in this manner.