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Previous: 2.3.2 Jacobi Relaxation
Somewhat faster convergent than Jacobi.
Choose
(i. e. lower triangle):
Solving the set of implicit equations
is almost as simple as solving the explicit Jacobi equations.
Since the matrices
and
are triangular the only
change is that in the downward recursion 2.1 some of the
right hand terms refer to the present iteration instead of the
previous, ; however, each term is available as soon as it is required.
EXAMPLE:
With the same data as in the previous example we find the
first two improved solutions
The convergence rate of the GSR scheme is governed by the matrix
It can be shown that the spectral radius of
is given by
so that the rate of convergence is now
In our example
and
.
Next: 2.3.4 Successive Over-Relaxation (SOR)
Up: 2.3 Iterative Methods
Previous: 2.3.2 Jacobi Relaxation
Franz J. Vesely Oct 2005
See also: "Computational Physics - An Introduction," Kluwer-Plenum 2001