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Given the Linear system

$$Ax = b$$

where $A$ is an $s$-sparse ($s$ is the maximum number of non-zero entries in $A$), $k$-conditioned ($k$ is the ratio between the highest and the smallest eigenvalue) matrix of size $N$, how can I express the time complexity of CG method based on those three parameters? I have found out different questions in Stack exchange (1,2), but none of them considers all three parameters.

emacs drives me nuts
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Macalcubo
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    CG is a method for systems of equations in which $A$ is symmetric and positive definite. Is your $A$ matrix symmetric and positive definite? – Brian Borchers Feb 10 '20 at 13:06
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    Thanks for your answer. Yes, my matrix is symmetric and positive definite. – Macalcubo Feb 10 '20 at 13:08
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    This is a duplicate of the first question you linked to, which correctly answers that it is $O(m \sqrt{\kappa})$. There's no direct dependence on $N$ but since $m>N$, this is dealt with. – Brian Borchers Feb 10 '20 at 13:10
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    How can it be m > N? m should be equal or lower than N. In the worst case the matrix is full then m=N, no? – Macalcubo Feb 10 '20 at 13:13
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    If the matrix is of size $N$ by $N$, then in order for it to be positive definite, $m$ must be greater than or equal to $N$ (all diagonal entries must be nonzero.) The matrix is full when $m=N^{2}$. – Brian Borchers Feb 10 '20 at 15:28

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