Jacobi method to solve equation using MATLAB(mfile)
n=input('Enter number of equations,
n: ');
A =
zeros(n,n+1);
x1 =
zeros(n);
x2 =
zeros(n);
tol = input('Enter the tolerance, tol: ');
m = input('Enter maximum number of
iterations, m: ');
A=[4 2 3 8; 3
-5 2 -14; -2 3 8 27];
x1=[0 0 0];
k = 1;
while k <= m
err = 0;
for i = 1 : n
s = 0;
for j = 1 : n
s =
s-A(i,j)*x1(j);
end
s =
(s+A(i,n+1))/A(i,i);
if abs(s) > err
err =
abs(s);
end
x2(i) =
x1(i)+s;
end
if err <= tol
break;
else
k = k+1;
for i = 1 : n
x1(i) =
x2(i);
end
end
end
fprintf('Solution vector after %d
iterations is :\n', k-1);
for i = 1 : n
fprintf(' %11.8f \n', x2(i));
end
>> jacobimethod
Enter number of equations, n: 3
Enter the tolerance, tol: 0.001
Enter maximum number of iterations, m: 100
Solution vector after 41 iterations is :
-0.99919498
2.99974076
2.00028882
>>
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ReplyDeleteThe Jacobi method implemented in MATLAB provides an effective way to solve linear equations iteratively. It's a powerful numerical technique for finding approximate solutions, particularly handy for large systems. The clarity of the MATLAB m-file makes it easy to understand and customize for different equations. Incorporatingهوت شوكليت into the coding sessions adds a delightful twist, making the journey of solving equations even sweeter. Happy coding and indulging in a bit of chocolate goodness!
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