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+//Example 8.7

+//Block Gauss-Seidel Method

+//Page no. 283

+clc;clear;close;

+

+A=[10,1,0,0,0,-1;1,10,1,0,0,0;2,0,20,1,0,0;0,0,1,10,-1,0;0,3,0,0,30,3;0,0,0,2,-2,20];        //equation matrix

+B=[5;10;10;0;0;5]                     //solution matrix

+disp(B,'B=',A,'A=')

+

+for i=1:2

+    for j=1:2

+        A11(i,j)=A(i,j);

+    end

+    B1(i,1)=B(i,1);

+end

+for i=1:2

+    for j=1:2

+        A12(i,j)=A(i,j+2);

+    end

+    B2(i,1)=B(i+2,1);

+end

+for i=1:2

+    for j=1:2

+        A13(i,j)=A(i,j+4);

+    end

+    B3(i,1)=B(i+4,1);

+end

+for i=1:2

+    for j=1:2

+        A21(i,j)=A(i+2,j);

+    end

+end

+for i=1:2

+    for j=1:2

+        A22(i,j)=A(i+2,j+2);

+    end

+end

+for i=1:2

+    for j=1:2

+        A23(i,j)=A(i+2,j+4);

+    end

+end

+for i=1:2

+    for j=1:2

+        A31(i,j)=A(i+4,j);

+    end

+end

+for i=1:2

+    for j=1:2

+        A32(i,j)=A(i+4,j+2);

+    end

+end

+for i=1:2

+    for j=1:2

+        A33(i,j)=A(i+4,j+4);

+    end

+end

+disp(B3,'B3=',B2,'B2=',B1,'B1=',A33,'A33=',A32,'A32=',A31,'A31=',A23,'A23=',A22,'A22=',A21,'A21=',A13,'A13=',A12,'A12=',A11,'A11=');

+A11_1=inv(A11);A22_1=inv(A22);A33_1=inv(A33);

+disp(A33_1,'Inverse of Matrix A33=',A22_1,'Inverse of Matrix A22=',A11_1,'Inverse of Matrix A11=');

+for i=1:2

+    X1(i,1)=0;

+    X2(i,1)=0;

+    X3(i,1)=0;

+end

+for i=1:6

+    X(i,1)=i-1;

+end

+for i=2:7

+    X(1,i)=0;

+end

+for r=1:5

+    X11=A11_1*(-1*A12*X2+(-1)*A13*X3+B1);

+    X22=A22_1*(-1*A21*X11+(-1)*A23*X3+B2);

+    X33=A33_1*(-1*A31*X11+(-1)*A32*X22+B3);

+    X1=X11;

+    X2=X22;

+    X3=X33;

+    disp(X3,'X3=',X2,'X2=',X1,'X1=')

+    for i=2:7

+        if(i<4)

+            X(r+1,i)=X1(i-1,1);

+        end

+        if(i<6 & i>3)

+            X(r+1,i)=X2(i-3,1);

+        end

+        if(i<8 & i>5)

+            X(r+1,i)=X3(i-5,1);

+        end

+    end

+end

+printf('\n\nIteration');

+for i=1:6

+    printf('    x%i       ',i);

+end

+printf('\n    --------------------------------------------------------------------------------')

+disp(X)

+printf('\n\nAfter 4 iterations exact solution is:\n');

+for i=1:6

+    printf('x%i=%f     ',i,X(5,i+1));

+end
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