🚀 go-pugleaf

In "Computational Methods of Linear Algebra," by D.K. Faddeev and 
V.N. Faddeeva, translated by Robert C. Williams, W. H. Freeman and 
Company, original publication date 1960, some methods for 
eigenvalue/eigenvector calculations are given.  In particular, the 
method of minimal iterations is given, along with a method of 
orthogonalization of columns method.  I want to pursue the 
calculation of eigenvectors from the orthogonalization of columns 
method, but I haven't worked out the polynomials that would 
correspond to this. 

A similar orthogonalization of rows method is cited as Johann 
Schroeder, Arch. Math., 1953, 4, 322-326.  My German isn't fluent, 
but I think this article should have cited with an earlier chapter.  
I remain unenlightened after viewing it.

Many of the references in this book are in the mid to late 50's, 
e.g. this was an active area of research at publication time.  One 
name that I recognized was J.L.Synge.  So I presume that more work 
is being done.

I'm wondering if there is more recent literature that someone could 
refer me to, or if someone has the polynomials worked out.  I'm 
somewhat excited about this, because the initial orthogonalization 
with pivoting has yielded essentially the correct eigenvalue and 
eigenvector spectrum of a 108x108 correlation matrix from some of my 
lab data, with only a trivial amount of computation time. Although I 
could code an iterative method today to refine these initial values, 
I would like to investigate an exact method.  

I'm looking for real-time with a 650x650 on a PC box...
-- 
Aubrey McIntosh  /  Chemistry  /  University of Texas  /  Austin, TX 78712
..another Gaelic learner...