Ill-posed equations with transformed argument.
Improving the convergence of iterative methods
The author considers the operator equation . Methods for acceleration of convergence of the iterative process are investigated.
Inverse problems in spaces of measures
The ill-posed problem of solving linear equations in the space of vector-valued finite Radon measures with Hilbert space data is considered. Approximate solutions are obtained by minimizing the Tikhonov functional with a total variation penalty. The well-posedness of this regularization method and further regularization properties are mentioned. Furthermore, a flexible numerical minimization algorithm is proposed which converges subsequentially in the weak* sense and with rate 𝒪(n-1)...
Iterative refinement for approximate eigenelements of compact operators
Iterative solution of eigenvalue problems for normal operators
We will discuss Kellogg's iterations in eigenvalue problems for normal operators. A certain generalisation of the convergence theorem is shown.