Approximate solutions to the following linear systems Ax = b to within 10−5 in the l∞ norm.
(i)
and
b = (1.902207, 1.051143, 1.175689, 3.480083, 0.819600,−0.264419, − 0.412789, 1.175689, 0.913337,−0.150209,−0.264419, 1.051143,1.966694, 0.913337, 0.819600, 1.902207)t
(ii)
and
b = (1, 0,−1, 0, 2, 1, 0,−1, 0, 2, 1, 0,−1, 0, 2, 1, 0,−1, 0, 2, 1, 0,−1, 0, 2)t
(iii)
And bi = 1.5i − 6, for each i = 1, 2, . . . , 40
a. Use the Jacobi method,
b. Use the Gauss-Seidel method,
c. Use the SOR method with ω = 1.3 in (i), ω = 1.2 in (ii), and ω = 1.1 in (iii).
d. Use the conjugate gradient method and preconditioning with C−1 = D−1/2.
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