| In this dissertation numerical solution methods for discrete linear ill-posed problems and inconsistent linear systems are studied. Several new methods are described and analyzed. Also numerical experiments are carried out to illustrate the performance of the methods.;For ill-posed problems, we first choose a filter function, then derive iterative methods to solve the problems. The iterative methods are based on Chebyshev polynomial expansions of the filter function. We calculate the regularization parameter, which determines the filter function, according to Morozov discrepancy principle.;Two new methods are presented for the solution of inconsistent linear systems. First, new orthodir implementations of conjugate gradient type methods are discussed. Second, we describe a semi-iterative method for the solution of inconsistent linear systems. This methods is based on the Leja-Richardson iteration and modified moments. |
