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What is the best known algorithmic complexity for computing the spectral radius (largest eigenvalue in magnitude, possibly with respect to some precision and confidence) of a symmetric matrix of size $d$, not sparse, and generally full rank, along with the prior knowledge that it is in a window $[a, b]$ ?

There are a few iterative algorithms that allow one to compute eigenvalues in order of decreasing magnitude such as power iteration, Lanczos, ... are some methods arguably better than others for this particular set up ?

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