Iterative Methods

Abstract

Iterative solution algorithms are described for complex systems with a large number of degrees of freedom. Areas of application include partial differential equations, integral equations, and hybrid methods in electromagnetics. Classical (or stationary) methods and conjugate gradient (nonstationary) methods are presented. Classical methods are generalized in terms of matrix splittings. The conjugate gradient method is derived in detail from the point of view of Galerkin testing and Krylov spaces. Preconditioning is discussed, and some common preconditioners from classical methods are presented.