Show that the Jacobi and Gauss-Seidel iterations converge, but that the iteration matrices J and GS have one-, two-, and infinity norms greater than or equal to 1. The matrix Let range from in...

Show that the Jacobi and Gauss-Seidel iterations converge, but that the iteration matrices

_J
and

_GS
have one-, two-, and infinity norms greater than or equal to 1.

The matrix

Let

range from

in steps of

and graph

vs.


_SOR

Do part

except graph

vs.

<sub>SOR

2</sub>

Comment on the results of parts