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Homework 10 Solution

# Homework 10 Solution - Lecture 10 MEEN 357 Homework...

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Lecture 10 MEEN 357 Homework Solution 1 Lecture-10-Homework-Solution-2009.doc RMB 1. Problem 12.1(a) of the textbook. Solution : You are asked to use the Gauss-Seidel method to solve 1 2 3 0.8 0.4 0 41 0.4 0.8 0.4 25 0 0.4 0.8 105 x x x ⎤⎡ ⎥⎢ = ⎥⎢ ⎥⎢ ⎦⎣ (10.1) You are instructed to continue the iteration until the percent relative error falls below 5% s ε = . You can work this problem by hand or by use of the function mfile GaussSeidel.m introduced in class. The solution here uses the function file. The MATLAB script %Problem 12.1a of the textbook. clc, clear all A=[0.8,-0.4,0;-0.4,0.8,-0.4;0,-0.4,0.8] b=[41;25;105] x0=[0;0;0] x=GaussSeidel(A,b,x0,5) yields the output x = 167.8711 239.1211 250.8105 in 6 iterations. The above solution starts the iteration at x0=[0;0;0] . A different starting point would produce the same answer in a different number of iterations. 2. Problem 12.2 of the textbook. Solution : The problem is essentially the same as the first one above except that the system of equations is 1 2 3 10 2 1 27 3 6 2 61.5 1 1 5 21.5 x x x ⎤⎡ ⎥⎢ = ⎥⎢ ⎥⎢ ⎦⎣ (10.2)

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Lecture 10 MEEN 357 Homework Solution 2 Lecture-10-Homework-Solution-2009.doc RMB As with the first problem above, you are instructed to continue the iteration until the
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Homework 10 Solution - Lecture 10 MEEN 357 Homework...

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