System of equations with sparse linear equations

Hello,

I have a sparse matrix A of size 65000x65000 only having 2's on the diagonal and 1's above and below the diagonal and the rest are zeros, and a system of equations in the form of X = A*B. The problem is that A is already a large matrix and MATLAB doesn't allow me to create such a vector to solve the equation.

Any ideas?

Answer 1

[Torsten]

B is the unknown vector, A and X are given ?

Note that B can be determined by backward substitution:

n = 65000;
B = zeros(n,1);
B(n) = 0.5*X(n);
for i = n-1:-1:1
  B(i) = (X(i)-B(i+1))*0.5
end

No need to form A explicitly.

Best wishes

Torsten.

[Ghady Hajj]

What is the 0.5 for. Just for clarification suppose that A is a 4x4 matrix it would look like this:

[2,1,0,0; 1,2,1,0; 0,1,2,1; 0,0,1,2]

How would your solution fit my matrix?

Thanks so much.

[Torsten]

If I'm not mistaken, you were first talking about a diagonal of 2's and 1's above the diagonal. Now I read that there are 1's also below the diagonal. For this case, the code from above does not work.

Try

http://www.math.iit.edu/~fass/matlab/html/TridisolveDemo.html

Best wishes

Torsten.

[Ghady Hajj]

Yeah sorry, that was a mistake, thank you!