HELP with creating matrix for Jacobi and Gauss-Seidel method problem!!

How can i create this matrix in matlab?

aij= [2i when j=i and i=1,2,...,80

0.5i when {j=i+2 and i=1,2,...,78 AND j=i-2 and i=3,4,...,80

0.25i when {j=i+4 and i=1,2,...,76 AND j=i-4 and i=5,6,...,80

0 otherwise]

and those of b are bi = π, for each i = 1,2,...,80.

I will need to use Jacobi and Gauss-seidel method to solve the linear system Ax = b to within 10−5 in the l∞ norm with the given matrix entries above. I am just stuck with how to create the matrix. I have spent so long reading the book and other sites but still have no idea where to even begin with the entries of this matrix so any help is appreciated!

[Dang Khoa]

After that, how can you create the matrix ? can you give me a code

Answer 1

[Daniel kiracofe]

the brute force approach would be something like this.

for i = 1:80
  for j = 1:80
    if (i==j)
       a(i,j) = 2*i;
    elseif ( other conditions)
       a(i,j) = whatever
    etc.
  end 
end

There are quicker ways to do it, but this will be easiest to understand. for 80x80 matrix, speed will not be an issue.

[equinox]

Thank you for the help! i was able to construct the matrix using this approach. However now i am a little confused on using the Jacobi and Gauss-seidel methods to solve the linear system Ax=b. Any tips or suggestions?

[Torsten]

Use "tril", "diag" and "triu" to build the appropriate iterations matrices L, D and U and solve the linear systems

L*x_new = b-U*x_old for Gauss-Seidel

and

D*x_new = b-(L+U)*x_old for Jacobi

using "backslash (\)".

Best wishes

Torsten.