Linear Regression

Hi there, Long time no see, sorry I have been rather quite taken with various business ventures and so I have not been working on my projects as much as I should have. As I have had a lot of downtime recently as the semester winds down I have been taking my free time at work to learn some celestial mechanics.

The notes I am using are great and so I will link to them here.  It starts off with a primer on numerical methods, one of the things he asks you to do is create a program which will compute the  least squares solution to an overdetermined system, then apply that program to create a least squares fit to a set of data. This was the method Gauss used to create tables of ephermrides for asteroids, but it presents and interesting set of computational problems,

1) how does one represent a matrix in memory
2) how does one solve a system of linear equations in a finite number of steps
3) how does one then use that solution as a polynomial to evaluate a coefficent of determination.

This has occupied my time on and off for the past couple of weeks. It suffices to say I learned a lot about representing mathematical objects in a computer. Polynomials are really quite facinating actually. For example it is possible to compute a polynomial at any unknown value in Ω(n) time where n is the degree of the polynomial.

Another interesting question is how does one test a linear least squares code once its been written. The answers are found in my github repository. Here I will only present my results:

The test data and fit

Polynomial model: 
Degree: 1
Coefficients:
a_1: 7.939715
a_0: 1438.362123
r: 0.997310
r²: 0.994628

Recipies Page

Hi All,

Apparently people are now interested in what I am eating, which I kind of do not understand but no matter. I have added a recipes page with my first recipe, a marinated London Broil which I may cook for this weekend again. Stay tuned for Teriyaki Salmon, Paleo-Pizza, and others. Find the link at the top.

Old Astrophotography

Hi all,

Its a double update! I was able to find an old flicker account that had all of my "best" astrophotos. These are the result of a misguided attempt to get into the game. It actually starts when I am a little boy...

See, I have always loved astronomy and so when I was little my parents would get me toy telescopes that would immediately break, they would also get me Astronomy magazines. In the back of these magazines you would see full page color advertisements for telescopes, one in particular struck my fancy. It was the LX200 with Magellan II controller, the first fully computerized GOTO telescope.

Fast forward to 2005 when I have finally scraped together enough dough to buy one. I decide to get it and the new Meade DSI II Pro monochrome camera which promises that you can take images in Alt-Az mode. (This is a lie, and never ever believe anyone who claims you can take "excellent" images with a telescope in an Alt-Az configuration.) In my case I hat a brain dump and got the 10" model. The results of a few imaging sessions are now on the astrophotography page of the website. I have tried to give the particulars of each image to the best of my recollection but the last imaging session I had was in the spring of 2007. (I think...)