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Quadrature refers to techniques in numerical integration, such as Riemann sum approximations, Simpson's rule and Gaussian quadrature.

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Change of Interval for Chebyshev–Gauss quadrature

I am curretly working to numerically evaluate an integral of the form: $$\int_{-1}^{1} f(x) \sqrt{1-x^2} dx$$ For this issue Gauss-Chebysehv integration of second kind seems ideal as it uses the ...
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Interleaving of Gaussian quadrature nodes and weights

A Gaussian quadrature is used to approximate the following integral: $$\int_{-1}^{1} f(x) dx \approx \sum_{i=1}^n w_i f(x_i).$$ Numerically I've found an interesting property of $x_i$ and $w_i$: if ...
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When can one trust that an adaptive quadrature scheme is not missing nontrivial areas of the domain?

hcubature http://ab-initio.mit.edu/wiki/index.php/Cubature_(Multi-dimensional_integration) seems to be a useful package for computing multidimensional integrals numerically. However, I have come upon ...
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Roughness of $\int\sqrt{1-t^2}f(t)\,dt$ in $[-1,1]$

Why is this integrand non-smooth in $[-1,1]$? $$\int\sqrt{1-t^2}f(t)\,dt$$ where $f$ possesses an analytic extinction to a complex neighbourhood $[-1,1]$ More general, how can I find it out? Thanks ...