Description
1. [7 pts] Use the Jacobi method to solve this system starting from a guess of [x1, x2, x3]
T =
[0, 0, 0]T
. Perform at least four iterations.
6×1 − 2×2 + x3 = 11
−2×1 + 7×2 + 2×3 = 5
x1 + 2×2 − 5×3 = −1
2. [10 pts] Use the Gauss-Seidel method to solve that same system from the same
guess. Perform at least four iterations. Does this appear to converge more quickly
than Jacobi? Should it?
3. Gaussian elimination vs. Gauss-Jordan:
(a) [4 pts] What is the difference between these methods, in terms of the way they
work (i.e., the algorithm)?
(b) [3 pts] Which one runs faster, for really large matrices? (Hint: check out section
2.1.2 of Sauer and think about how to modify that analysis for Gauss-Jordan.)
(c) [5 pts] How would you parallelize Gaussian elimination—i.e., what would you
have each processing unit doing?
(d) [5 pts] How would you parallelize Gauss-Jordan—i.e., what would you have
each processing unit doing?
4. [6 pts] Problem 4(b) on page 93 of the textbook.
5. [20 pts] Computer problem 4 on page 136 of the textbook. Please turn in a table
of the iterates (like the ones on page 133) and a copy of your code.
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