6 - Universality for the Toda Algorithm
Published online by Cambridge University Press: 24 October 2025
Summary
As noted in the Introduction, in this chapter we consider running the Toda algorithm only until time T(1), the deflation time with block decomposition k = 1 fixed, when the norm of the off-diagonal elements in the first row, and hence the first column, is O(ϵ)
. Define E(t)=∑n=2N|X1n(t)|2
so that if E(t)=0
then X11(t)
is an eigenvalue of H. Thus, with E(t)
as in (6.1), the halting time (or 1-deflation time) for the Toda algorithm is given by T(1)(H)=inf{t:E(t)≤ϵ2}
.
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- The Toda Lattice and Universality for the Computation of the Eigenvalues of a Random Matrix , pp. 129 - 151Publisher: Cambridge University PressPrint publication year: 2025
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