There exist many reliable methods of an efficient iterative
diagonalization of a real, n by n symmetric matrix $H$ where the
diagonal matrix elements dominate and are well separated.  In this
context, the author surprized me by having offered an interesting
new idea. In fact, it may summarized easily: after an
``introductory" standard triangular-matrix pre-factorization of
$H=LL^T$, the author notices that the solution (making $O H O^T$
diagonal) may be seen as equivalent to the search for the $n^2$
real matrix elements of the product $OL$ by the Newton-Kantorovich
method.

The numerical practicioner's community must be warned in advance:
With all probability the method working with the $n^2 \times
n^2-$dimensional matrices will prove neither useful nor efficient.
Indeed, the author describes his/her method by describing
thoroughly the n=3 case (and even this analysis is not
particularly short) and illustrates its application on a sparse
n=4 model. Nevertheless, I found an appeal of his/her proposal in
the proof of the exact convergence of the recipe under certain
assumptions.


MR2157097 Chkhartishvili, L. S. An iterative solution of the
secular equation. (Russian) Mat. Zametki 77 (2005), no. 2,
303--310; translation in Math. Notes 77 (2005), no. 1-2, 273--279