175	1996	Per Lötstedt	perl@tdb.uu.se	Convergence analysis of iterative methods by pseudodifference operators
 
                            Abstract

The convergence of iterative methods to solve linear partial differential
equations numerically is analyzed by the theory of pseudodifference
operators. Approximate inverses are determined from the symbol of the
iterative operator so that implicit and preconditioned methods are covered.
The behavior of the symbol for higher wave numbers describes the
convergence rate very well for the corresponding error modes. The results
are applied to Krylov subspace methods and stationary methods of
Gauss-Seidel type. For Krylov methods the convergence of the smooth part
of the error is given by global error estimates for numerical solution of
ordinary differential equations.

Keywords: pseudodifference operators, Fourier analysis, iterative methods,
partial differential equations, numerical solution, convergence

AMS subject classification: 65F10, 65N22