Tikhonov regularization for large-scale linear ill-posed problems is commonly implemented by determining a partial Lanczos bidiagonalization of the matrix of the given system of equations. This paper explores the possibility of instead computing a partial Arnoldi decomposition of the given matrix. Computed examples illustrate that this approach may require fewer matrix-vector product evaluation...

Abstract Tikhonov regularization with square-norm penalty for linear forward operators has been studied extensively in the literature. However, results on convergence theory are based technical proofs and sometimes difficult to interpret. It is also often not clear how those translate into discrete, numerical setting. In this paper we present a new strategy study properties of method example re...