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In numerical analysis Chebyshev–Gauss quadrature is an extension of Gaussian quadrature method for approximating the value of integrals of the following kind: ∫ − 1 + 1 f ( x ) 1 − x 2 d x {\displaystyle \int _{-1}^{+1}{\frac {f(x)}{\sqrt {1-x^{2}}}}\,dx}
In mathematics, a proof by infinite descent, also known as Fermat's method of descent, is a particular kind of proof by contradiction [1] used to show that a statement cannot possibly hold for any number, by showing that if the statement were to hold for a number, then the same would be true for a smaller number, leading to an infinite descent and ultimately a contradiction. [2]
In mathematics numerical analysis, the Nyström method [1] or quadrature method seeks the numerical solution of an integral equation by replacing the integral with a representative weighted sum. The continuous problem is broken into n {\displaystyle n} discrete intervals; quadrature or numerical integration determines the weights and locations ...
Copeland's method (voting systems) Crank–Nicolson method (numerical analysis) D'Hondt method (voting systems) D21 – Janeček method (voting system) Discrete element method (numerical analysis) Domain decomposition method (numerical analysis) Epidemiological methods; Euler's forward method; Explicit and implicit methods (numerical analysis)
The Gauss–Kronrod quadrature formula is an adaptive method for numerical integration. It is a variant of Gaussian quadrature , in which the evaluation points are chosen so that an accurate approximation can be computed by re-using the information produced by the computation of a less accurate approximation.
In mathematics, the direct method in the calculus of variations is a general method for constructing a proof of the existence of a minimizer for a given functional, [1] introduced by Stanisław Zaremba and David Hilbert around 1900. The method relies on methods of functional analysis and topology. As well as being used to prove the existence of ...
The Crank–Nicolson stencil for a 1D problem. In mathematics, especially the areas of numerical analysis concentrating on the numerical solution of partial differential equations, a stencil is a geometric arrangement of a nodal group that relate to the point of interest by using a numerical approximation routine.
More formulas of this nature can be given, as explained by Ramanujan's theory of elliptic functions to alternative bases. Perhaps the most notable hypergeometric inversions are the following two examples, involving the Ramanujan tau function τ {\displaystyle \tau } and the Fourier coefficients j {\displaystyle \mathrm {j} } of the J-invariant ...