An engineering approach to generalized conjugate gradient methods and beyond (Q1917417)

The authors give a simple introduction of generalized conjugate gradient methods for readers who are not experts in this field. They present an overview of various conjugate gradient-type methods with their characteristic properties. The nonsymmetric linear systems used in numerical experiments are obtained by discretization and linearization of a coarse model of Navier-Stokes equations for various magnitudes of the Reynolds number. Preconditioning ``from the left and from the right'' is discussed. Behaviour of \(\log (|r_k|/ |r_0|)\) and \(\log(|e_k|/|e_0|)\) is plotted and the methods are compared using obtained graphs.