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The Lanczos tri-diagonalization process is widely or even routinely used today. It is said that it is useful for obtaining the extremal eigenvalues, but useless for medium eigenvalues.

But who discovered this point? I suspect that Lanczos himself did not know this.

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    $\begingroup$ Lanczos himself already noted in An iteration method, p.263 (1950) that his original method on large matrices with dispersed eigenvalues will "drown out" smaller eigenvalues, and proposed countermeasures. Further analysis and refinements were done by Ojalvo-Newman and Paige in 1970s, see Lanczos algorithm. $\endgroup$
    – Conifold
    Mar 19 at 11:33

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