Given a large square matrix A and a sufficiently regular function f so that f(A) is well defined, we are interested in the approximation of the leading singular values and corresponding singular vectors of f(A), and in particular of ‖f(A)‖, where ‖ · ‖ is the matrix norm induced by the Euclidean vector norm. Since neither f(A) nor f(A)v can be computed exactly, we introduce and analyze an inexa...

Several numerical methods for the solution of large linear ill-posed problems combine Tikhonov regularization with an iterative method based on partial Lanczos bidiagonalization of the operator. This paper discusses the determination of the regularization parameter and the dimension of the Krylov subspace for this kind of methods. A method that requires a Krylov subspace of minimal dimension is...