MTH 343 · 7.3 Jacobi and Gauss–Seidel methods

Jacobi and Gauss–Seidel Lab

Enter a linear system Ax = b and a starting vector x(0), then step through the Jacobi and Gauss–Seidel methods one iteration at a time.

From the slides
Section 7.3 (9th edition)
Size n
System [A | b] and starting vector x(0)

Entries: integers, decimals or fractions such as −1/2.

Method

The formulas and the table of iterates show this method.

Type up to k = 1000.

At iteration k

Iteration k, one component at a time

Strictly diagonally dominant?

Stopping criterion

‖x(k) − x(k−1)‖∞ / ‖x(k)‖∞ <

Type 0.001, 1e-5 or 10^-5.

Stop at the first k where the approximate relative error is below TOL, as in Examples 1 and 3 of the textbook (l∞ norm, at most 1000 iterations).

Iterates