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contents/thomas_algorithm/thomas_algorithm.md

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s# Thomas Algorithm
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# Thomas Algorithm
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As alluded to in the [Gaussian Elimination chapter](../gaussian_elimination/gaussian_elimination.md), the Thomas Algorithm (or TDMA, Tri-Diagonal Matrix Algorithm) allows for programmers to **massively** cut the computational cost of their code from $$ O(n^3)$$ to $$O(n)$$ in certain cases!
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This is done by exploiting a particular case of Gaussian Elimination where the matrix looks like this:

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