I'm afraid there is an other problem with the reorthogonalization procedure.
After the symmetrical constraint for the C matrix, the article claims
that the product of M and its transpose, is C over -2. The whole story
afterwards is based on this "-2" for going on with the taylor approximation
of power -1/2.
However this is wrong. C over -1 does not imply a power of -1 (in which
case the assumption made would be right) but the inverse matrix! So what
should be really on the right side of the equation, should be the inverse
of C over 2!
Then, the aproximation should be about the square root of the M product,just
to find the inverse of C, and finally, one more inversion to reach C.
Thanks very much, I have always been very uneasy about this derivation and I welcome a chance to sort it out. One of my problems is working out which of the rules that we use in the algebra of real numbers can safely be used in matrix algebra?
Are you saying that the following equation is not necessarily true?:
[C]^-1 * [C]^-1 = [C]^-2
In the algebra of real numbers I guess the equivalent would be:
x^-1 * x^-1 = (1/x)*(1/x) = 1/(x^2) = x^(-2)
In other words for real numbers x^-1 is the multiplicative inverse and also works like a power.
I think I'm missing something obvious here, or doing something silly, but I can't work out what it is.