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I'm the little trashcan that could!


Aug
18
comment Making a conjecture concerning a certain upper-triangular matrix
@b.gatessucks: Yeah, I just wanted to show him how to solve the recurrence by hand, rather than by using Mathematica, since it sounded like his question was from a math course.
Aug
18
revised Making a conjecture concerning a certain upper-triangular matrix
added 1327 characters in body
Aug
18
answered Making a conjecture concerning a certain upper-triangular matrix
Aug
14
comment Can Mathematica solve my system of differential equations?
I don't think this is a bad question, but I suspect that it is not possible for Mathematica to solve this equation analytically. Do you know if there is an analytic solution for it? If not, you can always numerically solve it if you know what values of $a_1,a_2$ are.
Aug
13
comment Manipulate crashes after running 4 minutes
@MathLind: You can also provide a link to this question when talking with Wolfram support people, just so they can see what other people have tried, etc (if you haven't already).
Aug
12
comment Convoluting inverse square root with Gaussian
Ah, you're right, this is different.
Aug
12
accepted Incorrect result from Integrate
Aug
12
comment Convoluting inverse square root with Gaussian
Actually, I asked this exact question last year! It's a bug, according to Daniel Lichtblau. See link above.
Aug
12
comment Convoluting inverse square root with Gaussian
possible duplicate of Incorrect result from Integrate
Aug
11
comment How can I reduce computation time while still obtaining a good approximation for my function?
Hmm, I found the reason why the FFT computation is so bad. According to aip.de/groups/soe/local/numres/bookcpdf/c13-9.pdf (from "Numerical Recipes in C"), it is tempting but very often massively inaccurate from a numerical perspective to compute Fourier coefficients using the FFT! Quoting from the book, "It is a sobering exercise to implement equation (13.9.6) for an integral that can be done analytically, and to see just how bad it is. We recommend that you try it." They then go on to provide a higher-order interpolation scheme. I'll give it a shot when I have time.
Aug
10
comment How can I reduce computation time while still obtaining a good approximation for my function?
Ugh, this is so strange. The $\epsilon$ function is quite smooth, but getting the FFT coefficients to be accurate is surprisingly difficult, with $5000\times 5000$ sampling grid for less than 1% error...
Aug
10
comment How can I reduce computation time while still obtaining a good approximation for my function?
One other question: your $\epsilon$ and $f$ arrays look sort of like Fourier coefficients, but your function $\epsilon(p_x,p_y)$ is not periodic on the $[0,2\pi]\times[0,2\pi]$ interval, so they're technically not really Fourier coefficients. Is that correct?
Aug
10
comment How can I reduce computation time while still obtaining a good approximation for my function?
Yeah I think I can speed this up by a huge factor. I'll post in a while.
Aug
10
comment How can I reduce computation time while still obtaining a good approximation for my function?
Question: Is your notation $\int_0^{2\pi}dp_xdp_y$ a shorthand for double integral $\int_0^{2\pi}\int_0^{2\pi}dp_xdp_y$ over a square region?
Aug
10
comment How can I reduce computation time while still obtaining a good approximation for my function?
Since your $\epsilon_{mn}$ matrix is basically just the positive-frequency portion of the fast Fourier transform of the $\epsilon$ function, I feel like the use of NIntegrate might actually not even be necessary, and a much faster method may be available. I'll see what I can do and post an answer in a few hours if I can figure it out.
Aug
7
revised Importing Output from Linux mpstat to Calculate Aggregate and Per-CPU Averages, Creating Tables and Graphs
added 916 characters in body
Aug
7
answered Importing Output from Linux mpstat to Calculate Aggregate and Per-CPU Averages, Creating Tables and Graphs
Aug
7
answered Generating an Array of Vectors
Aug
5
comment How to set up the Fourier domain for a Fourier Transform?
One question: You say you multiply by $\exp(i k d)$, but then in your code you multiply by Exp[-I*d*Sqrt[k^2 - klist[[i]]^2]]. Which one is correct?
Aug
5
answered How to set up the Fourier domain for a Fourier Transform?