My Education
My Weekends
My Religion
My Information
My Guilty Pleasure
My Role Model
For Your Eyes
For Your Ears
For Your Palate
For Your Touch
For Your Gag Reflex
For The Love of God

Tuesday, November 18, 2003

I had forgotten exactly how far I'd come to the edge during my brief stint as an engineering major. The following are a number of excerpts from my final project in matrix methods:

On the difference between dynamic and static diagonalizations:
"Of course, just knowing that these work on such a small matrix doesn’t mean that we can determine absolute worth. For example, the dynamic shifted inverse power method of doom takes significantly more steps per iteration than the shifted inverse power method, but tends to converge much, much faster. If one were to simply look at time, it turns out that, in fact, it depends. Of course. The nondynamic method went faster (though possibly just due to machine speed – a larger matrix would be a better test, however the larger matrix felt it was it’s patriotic duty to kill the machine. Twice.) "

On the inability of my flimsy algorithm to converge
"Of course, right off, one has to be suspicious of a matrix which looks so very, very sketchy in terms of order. There does not seem to be any real, rational reason why we would use this matrix to test our code. There is.

By running this matrix through our original power method code, we get the following as an eigenvalue:


This is, well, not one. The eigenvalues (as calculated by, again, our friend eig(A) in Matlab) are ¼, -1/3, ½, 1, and –1. Of course, the problem we can see right off is that |1| = |-1|, so the code is simply unable to converge upon an eigenvalue, even after 100 iterations. It is lost like a penguin in a lava flow. Thankfully, we have all sorts of code to throw at this – and the other method we’ll try is the QR-factorization method"

Explaning why "(a/b)^n" works...
Obviously, as you take such a ratio raised to successively higher powers, one becomes dominant, and the code can return it. Lovely. Except that it requires us to have both: A) An eigenvalue which is larger in magnitude than every other eigenvalue and B) A clearly dominant eigenvalue, or else it could take (to steal from Carl Sagan) billions, and billions, and billions of iterations

I can't believe I got away with writing the way I did. I guess being able to form sentences was a skill most engineers lack :/

cranked out at 2:59 AM | |

template © elementopia 2003
Chicken and/or Waffles
Be Objective
Be Qualitative
Be Mindless
Be Heartless
Be Confused
Be Aware
The Lounge
Appellate Blog