Speaker
Description
We consider the numerical solution of linear operator equations involving compact operators. Since compact operators do not admit bounded inverses, the associated equations are ill-posed and require regularization. The Arnoldi process provides a natural framework for approximating a compact operator by a nearby operator of finite rank, thereby reducing the infinite-dimensional problem to a sequence of small, structured subproblems. Regularization is incorporated by applying Tikhonov’s method to the projected equations.
This work investigates theoretical properties of the resulting Arnoldi–Tikhonov approach, including convergence behavior and the influence of Krylov subspace dimension on the regularized solutions. Numerical experiments are presented to illustrate the theoretical results and to demonstrate the effectiveness of the method for representative compact operator equations.