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From: John D'Errico on 24 Apr 2010 14:54
James Waldby <no(a)no.no> wrote in message <hqv09k$vmu$2(a)news.eternal-september.org>...

> Actually, cost of sorting should be trivial, on both (1) a practical
> basis and (2) a relative-cost basis. (1): For example, my 2GHz
> machine takes about 150 microseconds to sort an array of 500 doubles.
> (2): Given an n x n array with n eigenvalues, the cost of sorting the
> n eigenvalues should not exceed O(n ln n), which for large n is swamped
> by the O(n^3) or O(n^2) cost, whichever it is, of computing them.
> [As I understand it, shifted-QR with deflation will have at least one
> O(n^3) step, an initial Hessenberg calculation, but if you somehow avoid
> that step, it will have an O(n^2) cost per implicit QR iteration.]

NO. The sort is not the point. Sorting does not solve the
problem of tracking eigenvalues that vary parametrically.

Speed is irrelevant if the sort gives the wrong answer.

John
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