Krylov Subspace Methods with a Twist

Krylov subspace methods are widely used iterative solvers for real or complex linear systems. In this talk, I will advocate that these methods should be viewed as more than just algorithms juggling matrices and vectors. Instead, with a view towards the setting behind the linear systems, we will systematically re-derive a general residual minimizing Krylov subspace method. This leads to a more general view on and implementation of GMRES and further surprises.