Overview on Solvers for Linear Equations and New Nonlinear Solvers

Ruediger Weiss

Computing Center, University of Karlsruhe, Germany

The principles of state-of-the-art iterative solvers are reviewed. It will be shown that modern solvers are based on the same ideas as the classical conjugate gradient algorithm. From this point of view it is easy to classify the variety of new methods and to give convergence estimates. By transferring the ideas of linear solvers to nonlinear solvers a whole family of new methods can be constructed. Theoretical results for these methods will be given. All numerical tests show that particular new techniques are faster than classical techniques.