Regularization of ill-posed problems in Banach spaces by pro-jection methods
We consider an ill-posed linear operator equation with an operator acting between Banach spaces. For nding approximation to the solution, projection methods with n-dimensional subspaces of the problem are employed. Besides general projection method, the least squares method and the least error method are discussed. In order to appropriately choose the dimension of the subspace, we consider a priori and a posteriori choices by the discrepancy principle and by the monotone error rule. Numerical examples concerning solving integral equations of the rst kind by collocation method will be given.
This is a joint work with U. Hamarik, B. Kaltenbacher and U. Kangro.