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  • 0 posts edited
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  • 14 votes cast
Dec
4
comment What are the 4th degree roots of $1$?
First, please use informative titles which relate to the question bodies. Second, this belongs on math.stackexchange as it is unrelated to physics. Third, googling "fourth root of one" gives many satisfactory answers, for example this one.
Aug
10
comment (Numerical) Integration in log space
@Ian, $Y_I$ is monotonically decreasing, and does vary over many orders of magnitude. I do not know the derivatives, $f'(x)$, but of course I could approximate them...
Feb
8
comment Numerical integration with divergent bounds
@Ian, you were right! Chebyshev-Gauss quadrature does seem to work fine. For posterity, scipy's integrate.quad
Feb
7
comment Numerical integration with divergent bounds
Thanks, g(x) is definitely non-negative throughout the domain of interest. I'll try to play around with the guassian quadrature some more!
Feb
7
comment Numerical integration with divergent bounds
@Ian, there's no analytic version of the function [$g(x)$ is based on data]. But for physical reasons, the integral between these bounds must be well defined.
Feb
7
comment Numerical integration with divergent bounds
Thanks @Ian, that's a very helpful hint. I'm not sure the order of divergence. Is there a numerical way to find out?The scipy package's built-in Gaussian quadrature method fails for my function, so I assume Chebyshev polynomials (which I think it uses?) in particular don't work.
Feb
7
comment Numerical integration with divergent bounds
Thanks! But I don't have an analytic expression for my function, it is purely numeric. I will amend my question to explain better.
Feb
7
comment Numerical integration with divergent bounds
@imranfat thats basically what I've already said. But, for the simplest numerical methods, you must evaluate your function at (or near) your endpoints to evaluate the integral.
Feb
7
comment Numerical integration with divergent bounds
Thanks, that's what I tried first --- but as I make the poorly-behaved regions smaller, the difference between left and right reimann sums diverges... so I still wasn't getting a good approximation
Apr
30
comment mental math: approximating fractional exponents
Thanks! Can you explain briefly how you're constructing $f(x)$?
Apr
30
comment mental math: approximating fractional exponents
Thanks! Can you remind me of the generalized form for binomials?
Mar
4
comment Calculate the fraction of volume of a rectilinear grid cell within some radius of the origin
@Bilou06 I'm looking for an exact solution, because I think it should exist... If I can't find it, I'll have to settle for numerical -- but for a large number of grid cells, that could be quite expensive I think.
Feb
24
comment What is the operator $\bigoplus$ in the context of function spaces?
Could you elaborate on what that means? Perhaps in an 'answer' ?
Feb
11
comment What is the etymology of 'sinc function'?
Interesting, and why 'cardinal' ?
Dec
28
comment Markov process vs. markov chain vs. random process vs. stochastic process vs. collection of random variables
Definitely, that is quite helpful! Thanks