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Recently, inverse problems have attracted more and more attention incomputational mathematics and become increasingly important in engineeringapplications. After the discretization, many of inverse problems are reduced tolinear systems. Due to the typical ill-posedness of inverse problems, thereduced linear systems are often ill-posed, especially when their scales arelarge. This brings great computational difficulty. Particularly, a smallperturbation in the right side of an ill-posed linear system may cause adramatical change in the solution. Therefore, regularization methods should beadopted for stable solutions. In this paper, a new class of acceleratediterative regularization methods is applied to solve this kind of large-scaleill-posed linear systems. An iterative scheme becomes a regularization methodonly when the iteration is early terminated. And a Morozov's discrepancyprinciple is applied for the stop criterion. Compared with the conventionalLandweber iteration, the new methods have acceleration effect, and can becompared to the well-known accelerated v-method and Nesterov method. From thenumerical results, it is observed that using appropriate discretizationschemes, the proposed methods even have better behavior when comparing withv-method and Nesterov method.

Solving Severely Ill-Posed Linear Systems with Time Discretization Based Iterative Regularization Methods