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//Example No. 8_03
//Gauss Seidel
//page no. 269
clear ; close ; clc ;
A = [ 3 1 ; 1 -3]
B = [ 5 ; 5 ]
disp('Using a matrix to display the results after each iteration, first row represents initial assumption')
X(1,1) = 0 , X(1,2) = 0 ;//initial assumption
maxit = 1000;//Maximum number of iterations
err = 0.0003 ;
disp('x1 = (5-x2)/3');
disp('x2 = (x1 - 5)/3');
for i = 2:maxit
X(i,1) = (5 - X(i-1,2))/3 ;
X(i,2) = (X(i,1) - 5)/3 ;
//Error Calculations
err1 =abs((X(i,1) - X(i-1,1))/X(i,1))
err2 =abs((X(i,2)- X(i-1,2))/X(i,2))
//Terminating Condition
if err >= err1 & err >= err2 then
printf('The system converges to the solution ( %f , %f ) in %d iterations\n',X(i,1),X(i,2),i-1 )
break
end
end
//calcution of true error i.e. difference between final result and results from each iteration
trueerr1 = abs(X(:,1) - X(i,1)*ones(i,1)) ;
trueerr2 = abs(X(:,2) - X(i,2)*ones(i,1)) ;
//displaying final results
D = [ X trueerr1 trueerr2] ;
disp(D)
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