Interesting tidbit for astronomers/computer buffs

Ok, I'm stuck at work and am absolutely bored, so I wrote this... :)

If you ever look at charts on orbits and such, you might notice that the numbers will be different depending on where you look. Why is that?

It's because the computers used to calculate it lie! No joke. Ah, so you thought computers were infallible and trustworthy? Guess again! They lie all the time.

How so? Well, there's a few different things that cause this. The problem lies in the computer's limited precision, how a computer rounds/truncates numbers which varies between different machines, and what sort of algorithm was used to process the matrices (which are frequently used in many kinds of scientific applications).

There's more than one way to skin a cat. Some algorithms (methods for solving a problem) are faster than others but are less accurate in particular situations. An interesting one is the Jacobi Algorithm which was pretty much tossed away and left unused because it was so slow. A few years ago it was realized that this particular method is well suited for parallel-processing applications and can give very accurate results... and the machines nowadays are fast enough to use it.

Small perturbations in the matrix can result in large changes in the result... depending on the situation... one particular algorithm may suffer whereas another would do ok.

Matrices can be ill-formed, "air-conditioned" so that they spit out complete garbage. This can be easily demonstrated with a mere 3x3 matrix, let alone a large... say 1000x1000 matrix. Again, different algorithms can produce different results.

You can give two computers with different architectures the exact same problem, and solve it the exact same way and get entirely different answers... because the two different machines handle floating point operations slightly differently...

So, different machines and different algorithms can produce different answers... this is why the orbit charts... and various other things can be different depending on where you look. To achieve the best results sometimes requires an expert in computational linear algebra to examine the problem and determine a method of attack... usually this doesn't happen... somebody was just keying in values into the computer and had no idea that computers are compulsive liars.

-Miscue

Very interesting.....I have no idea what the heck you were talking about, but the whole thing just fascinated me!

Eh... the math/computer speak stuff isn't really important... it's just interesting to know that computers have limitations like this.

Miscue, please come to my college and teach Data Structures and Algorithms!!! Maybe if you did I would still be a Computer Science major!! I understand everything you just said, but there is only one professor who teaches DS&A and I cannot understand the woman! Oh, teach Linear Algebra too!! The guy that teaches that is a WACKJOB!

But wow, you are a smart guy! :) :) :D

Bah, I'm just a bungler. The guys who are actually good at this stuff are out there... it's insane really.

Quote:

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Originally posted by udtseal
Miscue, please come to my college and teach Data Structures and Algorithms!!!

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Heh... of course there'd be that Paintball field trip :)Extra credit for eliminating the prof. :D!!!

I'm only a freshman in highschool and I almost understood mroe than half of that!

There's a whole world of numerical mathematics (as opposed to symbolic, like 2x=5) and computers are used in it because their very nature is to do stuff with numbers. Because computers are made by humans they are limited and when doing calculations with really big numbers or great precision, those limitations are met. I'm a programmer and have had to think these issues sometimes - luckily not very often in my line of coding ;)

Matrices by hand...evil...our math teacher made us do all the matrices by hand, even solve like 4 variable systems of equations using matrices by hand. Day after the test she shows us how to do it on the calculator...she thinks calculators are evil

There's always a by hand method... but the way you do it with a computer algorithm is not necessarily the same. (This isn't covered in a regular linear algebra class) For instance, there is a Cholesky Factorization, and a Cholesky Algorithm. Both produce the same result but go about it in different ways, one is well suited for a computer.