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Given an $n \times n$ matrix $A$, and an $n \times 1$ vector $b$, the conventional way of computing an $n \times 1$ vector $x$ such that $x=Ax+b$ is to use the following iterations: $$x_{k+1}=Ax_{k}+b.$$ Then, $x$ can be approximated by $x_k$ when $k$ is sufficiently large.

However, such an iteration would compute all entries of $x$. Now, I only need to compute the $p$ largest entries of $x$ (instead of solving all the entries of $x$), is there a faster way of finding the $p$ largest entries of $x_k$ to approximate those of $x$? Could everyone give some reference to this problem? Thank you!

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