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I have been trying to figure out the time complexity of the conjugate gradient method.

I have to solve a system of linear equations given by

$$Ax=b$$

where $A$ is a sparse, symmetric, positive definite matrix.

What would be the time complexity of the conjugate gradient method?

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$O(m\sqrt{k})$, where $m$ is the number of nonzero entries in $A$ and $k$ is its condition number.

See Chapter 10 in this excellent tutorial.

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