In Austria, already in 1988 a chair for Industrial Mathematics has been set up at the Johannes Kepler Universität Linz. Since 1997 the chair for Industrial Mathematics is the head an own institute. Its founder and first head until 2007 was Prof. Heinz Engl, who then has been followed up by Prof. Ronny Ramlau from 2008 until present.
Many problems in practice are so-called inverse problems: they are concerned with determining causes for a desired or an observed effect (e.g., computerized tomography, parameter identification, inverse heat conduction or diffusion problems).
Inverse problems most often are ill-posed. A consequence is that arbitrarily small changes in the data may lead to arbitrarily large changes in the solution. As in the numerical treatment of inverse problems data errors are inevitable, one has to use stabilizing procedures for successfully dealing with ill-posed problems, so-called regularization methods.
The Industrial Mathematics Institute has a long tradition in analysing regularization schemes. While in the eighties the emphasis lay on the analysis of regularization methods for linear ill-posed problems, in the last years results have been obtained for regularization methods for nonlinear ill-posed problems, covering both theoretical analysis and practical applications.
Beside its expertise in inverse and ill-posed problems, the Industrial Mathematics Institute also focuses on mathematical methods for phase reconstruction from different types of optical data. In particular, Indmath has an extensive experience in developing phase reconstruction methods for different types of AO systems on large telescopes. In addition to that Indmath has a long-standing experience in developing new wavefront reconstruction algorithms for astronomical adaptive optics.