omn123

4 ms·

1.
by omn123 13y ago
Consider, for example, calculating binomial coefficients mod a large number. It's not hard to realise that C(n,k+1) = (n-k)C(n,k)/(k+1) is one way to write the binomial coefficients. So if we want to compute C(10^10,50309) mod 10^
2.
by omn123 13y ago
I've alluded to this in other comments but a lot of the mathematics is linear algebra. As gaius mentions, check out the wikipedia article. There are plenty of linear algebra books out there. Recently I've really enjoyed the book b
3.
by omn123 13y ago
You are quite correct about stability but I didn't want to get into technical details. And indeed you bring up correctly that such numerical issues mustn’t be treated lightly. I don't do computer graphics and the matrices I deal w
4.
by omn123 13y ago
Well today I learned. I never knew that. Stupid mathematics and its inconsistent notation.
5.
by omn123 13y ago
I'm not implying yours are not unstable, it's just there is a chance it might be. Typically exact formulas exhibit such properties. LU decomposition is numerically stable, for the most part. You can run into problems with floating
6.
by omn123 13y ago
It is actually linear. a,b,c,d are the unknowns and x1 and x2 are the inputs. A bit confusing since normally x1,x2 denote the unknowns.
7.
by omn123 13y ago
It's worth pointing out that you should rarely, if ever, use exact formulas since there are a lot of problems with numerical stability amongst other things. Often it is faster to just numerically solve the system. For example, in your