Construction, analysis and implementation of iterative methods for large systems of linear equations

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Proposed is research in the areas of numerical linearalgebra and scientific computing. The focus is on Krylov subspacemethods, an important and widely used class of iterative methodsfor solving large and sparse linear algebraic systems. The lasttwo decades have seen an explosion of research activity on thesemethods which was spurred by the need to solve systems of vastlyincreasing dimensions in many areas of science and engineering.This development was mainly devoted to theconstruction rather than the analysis of methods. We intend to improve the understanding of the principles behind Krylov subspace methods particularly for nonsymmetric linear systems and thereby tocontribute to a much needed thorough analyticfoundation. While the analysis of Krylov subspace methods isinteresting from a mathematical point of view, it is alsoessential for the success of the methods in practice. We wantto utilize new insights for solving linear systems arising inseveral real-world and large-scale applications, includingconstraint optimization and radiation transportproblems. Simultaneously, the applications will guide us in ourtheoretical work.