turkmath.org

The Matlab package IR Tools provides implementations of a range of iterative solvers for linear inverse problems, and a set of large-scale test problems in the form of discretizations of 2D linear inverse problems. We include iterative regularization methods where the regularization is due to the semi-convergence, and Tikhonov-type formulations where the regularization is due to a regularization term. In both cases, we can impose bound constraints on the solution. We implemented the iterative methods in a flexible fashion that allows the problem's coefficient matrix to be available as a (sparse) matrix, a function handle, or an object. The basic call to all of the iterative methods requires only this matrix and the right-hand side. Our codes automatically set default parameters of the stopping rules, regularization parameters, etc.; with an optional input structure, the user has full control of any of these algorithm parameters. The test problems represent realistic large-scale problems found in image reconstruction and several other applications. These new test problems replace the small and outdated test problems from 1994 in Regularization Tools. The basic call to all of the test problem generators produces a matrix, a right-hand side and the corresponding exact solution. Similar to the iterative methods, the user can use an optional input structure to control specific features of the test problem. This is joint work with Silvia Gazzola and James G. Nagy.