Anonymous at Mon, 3 Jun 2024 14:12:39 UTC No. 16207838

>>16207835
Do you have a strong grasp of basic analysis?

Anonymous at Mon, 3 Jun 2024 14:13:06 UTC No. 16207839

>>16207838
I like to think so, yes

Anonymous at Mon, 3 Jun 2024 16:47:07 UTC No. 16207983

>>16207839
If you get filtered by it then you don't. Numerics is literaly the ooga booga way of tackling analytical problems instead of elegant high IQ solutions

Anonymous at Mon, 3 Jun 2024 17:16:51 UTC No. 16208007

>>16207835
On coding? Practice recursion problems.
On problem/method conditioning or big O asymptotic stuff? Write it all out as formal notes, memorize it before the tests.
I really like numerical analysis. So practical

Anonymous at Mon, 3 Jun 2024 17:19:52 UTC No. 16208009

>>16208007
On paper theory proofs

Anonymous at Mon, 3 Jun 2024 17:25:31 UTC No. 16208017

>>16208009
What stuff you trying to prove? Like give an example? Like prove LU decomp works?

Anonymous at Mon, 3 Jun 2024 17:38:54 UTC No. 16208054

>>16208017
Well, currently I am studying quadratures, here's an example of what I have to do: find the quadrature formula, find the coefficients and the remainder. I sketched this out myself and I got a contradiction in the resulting system so I guess I do suck at both algebra and analysis

Anonymous at Mon, 3 Jun 2024 17:42:02 UTC No. 16208060

>>16208054
Oh that's not proof? That's just do what the computer should do.
Uh, have you studied the polynomial interpolation? That is pretty necessary before you integrate

Anonymous at Mon, 3 Jun 2024 17:43:40 UTC No. 16208065

>>16208060
When you get how to interpolate polynomials, then understanding the essence of quadrature is easy. Memorizing the different rules is a write-everything-down-in-your-notes thing that you study before tests.

Anonymous at Mon, 3 Jun 2024 17:47:00 UTC No. 16208071

>>16208060
>>16208065
Oh no, I am not trying to prove anything as in an actual published proof, sorry if I misled you. Yes, I have studied interpolation, but I suppose I still have some gaps in my knowledge. Do you recommend any other books? Currently, I'm going through pic rel

Anonymous at Mon, 3 Jun 2024 17:53:07 UTC No. 16208081

>>16208071
Im downloading your book rn, but Im sure it's in there. For your problem, you could just look up improper integral quadrature numerical analysis or something. Idk what stuff you're trying to do. Maybe do a variable change to make the bounds finite like t = -logx

Anonymous at Mon, 3 Jun 2024 17:56:32 UTC No. 16208089

>>16208081
or maybe t^2 = -logx

Anonymous at Mon, 3 Jun 2024 18:00:01 UTC No. 16208096

>>16208081
The book has a chapter about interpolation, I was asking if you know of any other books better than this one.

Anonymous at Mon, 3 Jun 2024 18:05:05 UTC No. 16208105

>>16208096
Im looking through it and it looks very good. Almost hand-holdy with pictures and shit. Can't think of anything that would be better.

Gives the same adv I did. Look through the book to solve your problem

Anonymous at Mon, 3 Jun 2024 18:05:52 UTC No. 16208106

>>16208105
Ah alright, then

Anonymous at Mon, 3 Jun 2024 18:47:38 UTC No. 16208194

>>16208054
Construct orthogonal polynomials.
The zeros of the second order polynomial will be the sample points.
p0 = 1
p1 = t-1/sqrt(pi)
p2 = t^2 - t*sqrt(pi)/(pi-2) + 1/(pi-2)-1/2
Sample at the roots of p2
weights satisfy:
w1+w2 = sqrt(pi)/2
w1*r1 + w2*r2 = 1/2

This will give the exact result for deg<4

Anonymous at Mon, 3 Jun 2024 19:10:42 UTC No. 16208218

>>16208194
r1 = [sqrt(pi) - sqrt(16 - 11*pi + 2*(pi)^2)]/(2*(pi - 2))
r2 = [sqrt(pi) + sqrt(16 - 11*pi + 2*(pi)^2)]/(2*(pi - 2))
w1 = (1/4)* [sqrt(pi) + (4 - pi)/sqrt(16 - 11*pi + 2*(pi)^2)]
w2 = (1/4)* [sqrt(pi) - (4 - pi)/sqrt(16 - 11*pi + 2*(pi)^2)]

Anonymous at Tue, 4 Jun 2024 03:50:48 UTC No. 16209088

>>16207835
learn to count