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//Eg-3.19
//pg-123
clear
clc
A=[4 2 0;0.5 1 .5;0 3 3];
B=[2.3;1.1;14];
es=10^-7;
imax=100;
X=[0;0;0];
iter=1;
lambda=1;
[r,c] = size(A)
n = r;
errorcheck=1;
//Gauss-Seidel Method
while errorcheck==1//condition for termination
for i=1:n
summ=B(i);
pivot=A(i,i);
if pivot==0
error('gsie not applicable');//to avoid a/0 forms
end
old=X(i);
for j=1:n
if i~=j
summ=summ-A(i,j)*X(j);
end
end
X(i)=(lambda*summ/pivot)+(1-lambda)*old;//relaxation
if X(i)~=0 then
AbsErr=abs((X(i)-old)/X(i))*100;//absolute error
else
output=('error cannot be computed')//since xi cant be equal to zero
end
if AbsErr<es
errorcheck=2;
end
end
iter=iter+1;
end
disp("solution Vector")
disp(X)
disp("iterations required for gauss siedel")
disp(iter)
iter=1;
lambda=1.5;
errorcheck=1;
X=[0;0;0];
//Gauss Siedel method with SOR
while errorcheck==1//condition for termination
for i=1:n
summ=B(i);
pivot=A(i,i);
if pivot==0
error('gsie not applicable');//to avoid a/0 forms
end
old=X(i);
for j=1:n
if i~=j
summ=summ-A(i,j)*X(j);
end
end
X(i)=(lambda*summ/pivot)+(1-lambda)*old;//relaxation
if errorcheck==1&X(i)~=0 then
AbsErr=abs((X(i)-old)/X(i))*100;//absolute error
else
output=('error cannot be computed')//since xi cant be equal to zero
end
if AbsErr<es
errorcheck=2;
end
end
iter=iter+1;
end
disp("solution Vector")
disp(X)
disp("iterations required for gauss siedel with SOR")
disp(iter)
disp("these results indicate how the convergence is expedited by over-relaxation")
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