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Aug
25
awarded  Popular Question
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...
Aug
10
asked (Numerical) Integration in log space
Mar
21
awarded  Notable Question
Feb
12
accepted What is the etymology of 'sinc function'?
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
awarded  Commentator
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
revised Numerical integration with divergent bounds
added 417 characters in body
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
revised Numerical integration with divergent bounds
added 571 characters in body
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
Feb
7
asked Numerical integration with divergent bounds
Jan
16
awarded  Notable Question
Jan
6
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17
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Sep
24
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