Read: text, through Chapter 4, to complete this assignment.

Reconsider Problem Set 1 and solve it with Jacobi, Gauss-Seidel and “optimal” SOR point iterative methods for N = 10, 20, 40 and 80.

In each case,

- Estimate the spectral radius and convergence rate,
- Report the number of iterations required to reach a fixed convergence criterion, and
- Tabulate the RMS error for each solution with each iterative method.

Discuss whether your results agree with theory relative to the convergence and convergence rates of the 3 solvers and with respect to the accuracy of your solutions as a function of N.

**EXTRA CREDIT:**

NOTES: The Thomas solver uses 3 1-D arrays, A(N) = subdiagonal, B(N) = diagonal, C(N) = superdiagnonal, plus R(N), the right-hand-side. Call Thomas with KKK=1 a single time, once the arrays are filled with the matrix coefficients, then use KKK=2 in your line iteration loop for computing the back-substitution with each new right-hand side at each iteration. As with Solve.f, the solution is returned in vector R(N) for each subroutine call with KKK=2.

**EXTRA EXTRA CREDIT:**