# Fastest method for solving diagonally dominant matrix

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• November 9th 2013, 11:30 AM
Nforce
Fastest method for solving diagonally dominant matrix
What is the fastest method in $O(n)$ notation for solving a matrix $A$. If I know that matrix $A$ 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.
• November 10th 2013, 02:36 AM
Bestwebuys
Re: Fastest method for solving diagonally dominant matrix
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• November 10th 2013, 06:16 AM
HallsofIvy
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.
• November 10th 2013, 06:36 AM
emakarov
Re: Fastest method for solving diagonally dominant matrix
There is the tridiagonal matrix algorithm, which works in time O(n).