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Also called numerical integration, quadrature refers to the approximation of an integral made by evaluating the integrand at a finite number of points.

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### Are there standard methods for joining a numerical function approximation to its asymptotic behavior?

I'm working on an algorithm for computing a function that is a generalization of the Voigt profile. The Voigt profile is the convolution of a Cauchy (aka Lorentzian) probability density function (PDF) ...
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### 3D Quadrature schemes with points on boundary

In one dimension there are two types of quadrature schemes. asymmetric rules like Newton-Cotes like formulas (Trapezodi, Simpson), and Clenshaw-Curtis place sampling points on boundary of the ...
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### Quadrature rules for products of 2D regions

I am interested in computing integrals of the form $\iint_{P\times P} Q(x_1,x_2,y_2,y_2) dxdy$ where $P$ is a polygon and $Q$ is a polynomial. The coordinates $(x_1,x_2)$ are in the plane of $P$. Of ...
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### Which way is the right way to compute the integrals in finite element methods?

Finite element methods involve integrals of functions that are not polynomials, and these integrals must be computed numerically. For example, suppose that $f$ is the right-hand side of a Poisson ...
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