- Ronny Ramlau, University of Linz,
- Elena Resmerita, AAU
- Kirk Soodhalter, University of Linz

" Iterative Methods for Ill-posed Problems"

Ill-posed problems are characterized by a discontinuous dependence of the solution on the input data. Since the input data generally come from real-world measurements, they will be contaminated with noise, rendering the solutions obtained from the usual linear solver techniques unreliable.

Regularization techniques are used to modify an ill-posed problem, yielding a nearby problem that can then be solved stably. Often, these problems are described by large-scale equations with sparse operators. In this setting, direct solvers can be computationally too demanding. Iterative techniques have been shown to produce high-quality solutions but without the computational demands of direct solvers. Since the operator may not be stored in memory (i.e., we may only possess a procedure which applies the operator), we generally consider matrix-free iterative methods.

Thus, there is an interface between research into iterative linear solvers and that of regularization of ill-posed problems. There have been many recent developments in the field of iterative methods which are not widely known in the regularization community. Conversely, many questions arise in the regularization community which could spur further research in the iterative methods community.

The goal of this minisymposium is to bring researchers together from these two communities to foster exchange of ideas and allow researchers from different fields to bring their unique perspectives to current research questions.

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