Show that the matrix is positive definite. Compute JGS and SOR Project a ranking for the number of iterations required by the methods. Generate a random vector and solve using all three...

Show that the matrix

is positive definite.

Compute

<sub>J

GS</sub>

and

_SOR


Project a ranking for the number of iterations required by the methods.

Generate a random

vector

and solve

using all three methods. Are your projections in part

correct

For the matrix compute the spectral radius of


<sub>J



GS</sub>
, and


_SOR

Will any of the iterative methods converge. Try one and see what happens.