Page 240 - MATLAB an introduction with applications

Numerical Methods ——— 225

Example E4.9: Find the solution to the equations using Gauss-Seidel method.

x
 42 00   4

1


 28 2 0  

x
0 
   =  
2
 02 8 2   
x
0
3
 
x
  0024   0 
  
 
4
Solution:
MATLAB Solution Using built-in function]:
>> A = [4 2 0 0;2 8 2 0;0 2 8 2;0 0 2 4];
>> B = [4;0;0;0];
>> x = A\B
x =
1.1556
–0.3111
0.0889
–0.0444
>> x=inv(A)*B
x =
1.1556
–0.3111
0.0889
–0.0444
>> A = [4 2 0 0;2 8 2 0;0 2 8 2;0 0 2 4];
>> b = [4;0;0;0];
>> tol = 1.0e – 9;
>> format long;
>> xguess = [1– 0.5 0.1 – 0.2];
>> [x,iter] = GAUSSD(A,b,xguess,tol)
x =
1.15555555568491 –0.31111111117579 0.08888888892123 –0.04444444446061
iter =
16
function [Y,iter] = GAUSSD(A,r,yguess,tol)
% GAUSSD will iteratively solve Ay = r
n = length(r); Y = yguess; dy = ones(n,1); iter = 0;
while norm(dy)/norm(Y) > tol
for i = 1:n
if abs(A(i,i))<100*eps;error(‘zero pivot found’);end
dy(i) = r(i)/A(i,i);