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# Tridiagonal matrix (thomas algorithm)

Asked by Mehmet on 11 Mar 2011

hi.

i want to solve a second order, homogeneous differential equation by using tridiagonal matrix. can u help me?

so, i want only a general matlab code to solve like this equation.

because i am using "finite difference method"

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Answer by John D'Errico on 11 Mar 2011

Why not just build it as a sparse matrix using spdiags, then solve using backslash? It will be quite fast for a tridiagonal matrix, and you won't need to write any solver at all.

For example, I won't bother to do more than create a random tridiagonal matrix, rather than building one directly from your equation, but the time is all that matters.

```n = 100000;
A = spdiags(rand(n,3),-1:1,n,n);
b = rand(n,1);
tic,x = A\b;toc
Elapsed time is 0.023090 seconds.
```

So to solve a system with 1e5 unknowns took me .023 seconds, with virtually NO time invested to write anything.

Mehmet on 11 Mar 2011