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+//Example 8.5
+//Gauss-Seidel Point Iterative Method
+//Page no. 279
+clc;clear;close;
+
+A=[2,3,-4,1;1,-2,-5,1;5,-3,1,-4;10,2,-1,2];       //equation matrix
+B=[3;2;1;-4];          //solution matrix
+
+//transformation of the equations
+for i=1:4
+    A1(1,i)=A(4,i);
+    B1(1,1)=B(4,1);
+end
+for i=1:4
+    A1(3,i)=A(2,i);
+    B1(3,1)=B(2,1);
+end
+for i=1:4
+    A1(2,i)=A(1,i)-A(2,i);
+    B1(2,1)=B(1,1)-B(2,1);
+end
+for i=1:4
+    A1(4,i)=2*A(1,i)-A(2,i)+2*A(3,i)-A(4,i);
+    B1(4,1)=2*B(1,1)-B(2,1)+2*B(3,1)-B(4,1);
+end
+
+//printing of transformed equations
+printf('\nTransformed Equations are=\n\n')
+for i=1:4
+    for j=1:4
+        printf('(%ix(%i))',A1(i,j),j);
+        if(j<4)
+            printf(' + ')
+        end
+    end
+    printf('= %i\n',B1(i,1));
+end
+
+for i=1:4
+    for j=1:4
+        if(A(j,j)==0)
+            for k=1:4
+                C(j,k)=A(j,k);
+                A(j,k)=A(j+1,k);
+                A(j+1,k)=C(j,k);
+            end
+        end
+    end
+end
+for i=0:12
+    X(i+1,1)=i;
+end
+for i=2:5
+    X(1,i)=0;
+end
+for r=1:12
+    for i=1:4
+        k1=0;
+        for j=1:i-1
+            
+                k1=k1-A1(i,j)*X(r+1,j+1);
+            
+        end
+        k2=0;
+        for j=i+1:4
+            
+                k2=k2-A1(i,j)*X(r,j+1);
+            
+        end
+        X(r+1,i+1)=(k1+k2+B1(i,1))/A1(i,i);
+    end
+end
+printf('\n\n    r     ');
+for i=1:4
+    printf('x%i           ',i);
+end
+printf('\n    ------------------------------------------------------')
+disp(X)
+printf('\n\nAfter 11 iterations exact solution is:\n');
+for i=1:4
+    printf('x%i=%f     ',i,X(12,i+1));
+end