Johannes Middeke, Research Institute for Symbolic Computation, Linz

Using Computer Experiments as Guidelines for Discoveries in Symbolic Linear Algebra

In our recent project we have tackled the surprisingly frequent occurrence of common row factors in Bareiss' fraction-free algorithm for matrix LU decomposition. We used computer experiments to first confirm the existence of those factors and then to gain an idea about how they arise. We applied similar methods to the fraction-free QR decomposition. In this talk, we discuss our approach to incorporate experimental methods in finding rigorous proofs.