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Gauss–Kronrod rules are extensions of Gauss quadrature rules generated by adding n + 1 points to an n-point rule in such a way that the resulting rule is of order 2n + 1. This allows for computing higher-order estimates while re-using the function values of a lower-order estimate.
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In numerical analysis Gauss–Laguerre quadrature (named after Carl Friedrich Gauss and Edmond Laguerre) is an extension of the Gaussian quadrature method for approximating the value of integrals of the following kind: + (). In this case
The figure on the right was created using A = 1, x 0 = 0, y 0 = 0, σ x = σ y = 1. The volume under the Gaussian function is given by V = ∫ − ∞ ∞ ∫ − ∞ ∞ f ( x , y ) d x d y = 2 π A σ X σ Y . {\displaystyle V=\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }f(x,y)\,dx\,dy=2\pi A\sigma _{X}\sigma _{Y}.}
Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]
The gauss is the unit of magnetic flux density B in the system of Gaussian units and is equal to Mx/cm 2 or g/Bi/s 2, while the oersted is the unit of H-field. One tesla (T) corresponds to 10 4 gauss, and one ampere (A) per metre corresponds to 4π × 10 −3 oersted.
Download as PDF; Printable version; In other projects ... Gauss–Chebyshev type 1 quadrature and Gauss–Chebyshev type 2 quadrature, free software in C++, Fortran, ...
The entry 4+2i = −i(1+i) 2 (2+i), for example, could also be written as 4+2i= (1+i) 2 (1−2i). The entries in the table resolve this ambiguity by the following convention: the factors are primes in the right complex half plane with absolute value of the real part larger than or equal to the absolute value of the imaginary part.