AN ENGINEERING APPROACH TO GENERALIZED CONJUGATE-GRADIENT METHODS ANDBEYOND

This is an elementary introductory paper (rather a tutorial) for gener alized conjugate gradient (CG) methods. The emphasis is on ''understan ding'' the approach of the now rather sophisticated CG-type methods an d beyond. Practical aspects like normalization and smoothing are discu ssed. Then the development of different types of methods with their ch aracteristic properties is presented. For a model of the Navier-Stokes equations that varies between strong and weak ellipticity, the method s are compared and their typical properties are demonstrated.