# Thread: Fastest method for solving diagonally dominant matrix

1. ## Fastest method for solving diagonally dominant matrix

What is the fastest method in $\displaystyle O(n)$ notation for solving a matrix $\displaystyle A$. If I know that matrix $\displaystyle A$ is diagonally dominant and tridiagonal matrix. Is it LU decompositon or Gauss-Seidel method, or some combination of both? Or is it something else?

Thank you for your help.

2. ## Re: Fastest method for solving diagonally dominant matrix

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3. ## Re: Fastest method for solving diagonally dominant matrix

I'm not sure what you mean by "solving" a matrix. If you mean solving an equation such as Ax= b, where A is a diagonally dominant, tri-diagonal matrix, "LU decomposition" of A should be simple and straight forward- probably simpler than Gauss-Seidel, but they are very nearly the same thing here.

4. ## Re: Fastest method for solving diagonally dominant matrix

There is the tridiagonal matrix algorithm, which works in time O(n).