This is a collection of routines comparing different iterative schemes 
for approximating the solution of a system of linear equations.

The schemes solve the system arising from the standard
FD/FE discretization of the Poisson equation with zero right hand
side on the unit square.

The routine compare_it.m plots the number of iterations needed
until the error reaches a specified tolerance versus the number of 
unknowns. Its usage is

	compare_it(TOL, Nmax)

where TOL is the specified tolerance, and 
Nmax is the maximum number of unknowns in ONE direction.

The routine compare_err.m plots the error decay versus the
number of iterations. Its usage is

	compare_err(TOL, N)

where TOL is the specified tolerance, and 
N is the number of unknowns in ONE direction.

The functions jacobi.m, gs.m, sgs.m, cong.m, are implementations of 
the associated solvers. Their usage is

	[it, err] = solver(A, f, x0, max_iter, TOL)

where	A 		is the system matrix,
	f 		is the right hand side,
	x0		is the start iterate,
	max_iter	is the maximum number of iterations,
	TOL		is the specified tolerance.

They return	it	the number of iterations needed,
		err	a vector of length it containing the error after 
			each iteration step.

If the right hand side f is zero, err is simply the norm of the iterate. 
For non-zero right hand sides, err is the weighted residual norm.

WARNING: The implementation was done following one rule: Keep it
simple and clear. Therefore the iterative schemes are by no means
implemented in an efficient way. To avoid overlong waiting
periods the number of unknowns be kept small.

Date: 2002-08-05
Author: Bernd Flemisch
Email: flemisch@mathematik.uni-stuttgart.de



