ENGR 351 NUMERICAL METHODS FOR ENGINEERS
Fall 2009
College of Engineering
Instructor: L.R. Chevalier, Ph.D., P.E.
Due October 16, 2009
HOMEWORK 3B
Overview:
This homework will continue your study of the Gauss Seidel and Jacobi matrix methods. If you did not understand
part a, I recommend that you see me or the graduate teaching assistant.
PROBLEM 1
Design a spreadsheet to calculate a matrix using both Gauss Seidel and Jacobi with relaxation. The spreadsheet
should be designed to input a 3x3 matrix, a value of , and the initial estimates for {x}.
Evaluate the following set of equations. Use an initial estimate of {x}T = {1 1 1}
2−9 3
−1−3 9
4 3 1 𝑥1
𝑥2
𝑥3 = −3
12
7
EXTRA CREDIT
This extra credit problem will require a more in-depth analysis of either the Jacobi or the Gauss Seidel method.
Specifically, you will develop graphs that will show if a is decreasing or x is converging. This is an open-ended
problem, which is important for engineering students to tackle.
1) The first part will require two graphs of your method without relaxation , using a diagonally dominant
matrix. Decide which value of x you will monitor (you are not required to do all three, but you may want
to). Provide a graph that shows how your value of x changes, and the corresponding value of a. For this
assignment, do not use the absolute value of a. This will allow you to see oscillations if they occur. Two
example graphs are shown below.
