1 files changed, 90 insertions, 0 deletions
diff --git a/260/CH3/EX3.19/3_19.sce b/260/CH3/EX3.19/3_19.sce
new file mode 100644
index 000000000..ab41a657c
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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")
+\ No newline at end of file