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  • 14 votes cast
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