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Tanh-sinh, exp-sinh, and sinh-sinh quadrature are implemented in the C++ library Boost [3] Tanh-sinh quadrature is implemented in a macro-enabled Excel spreadsheet by Graeme Dennes. [4] Tanh-sinh quadrature is implemented in the Haskell package integration. [5] Tanh-sinh quadrature is implemented in the Python library mpmath. [6]
It is assumed that the value of a function f defined on [,] is known at + equally spaced points: < < <.There are two classes of Newton–Cotes quadrature: they are called "closed" when = and =, i.e. they use the function values at the interval endpoints, and "open" when > and <, i.e. they do not use the function values at the endpoints.
The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for "numerical integration", especially as applied to one-dimensional integrals. Some authors refer to numerical integration over more than one dimension as cubature ; [ 1 ] others take "quadrature" to include higher-dimensional integration.
The two amplitude-modulated sinusoids are known as the in-phase (I) and quadrature (Q) components, which describes their relationships with the amplitude- and phase-modulated carrier. [ A ] [ 2 ] Or in other words, it is possible to create an arbitrarily phase-shifted sine wave, by mixing together two sine waves that are 90° out of phase in ...
Quadrature amplitude modulation (QAM), a modulation method of using both an (in-phase) carrier wave and a 'quadrature' carrier wave that is 90° out of phase with the main, or in-phase, carrier Quadrature phase-shift keying (QPSK), a phase-shift keying of using four quadrate points on the constellation diagram, equispaced around a circle
Also known as Lobatto quadrature, [7] named after Dutch mathematician Rehuel Lobatto. It is similar to Gaussian quadrature with the following differences: The integration points include the end points of the integration interval. It is accurate for polynomials up to degree 2n – 3, where n is the number of integration points. [8]
Routines for Gauss–Kronrod quadrature are provided by the QUADPACK library, the GNU Scientific Library, the NAG Numerical Libraries, R, [2] the C++ library Boost., [3] as well as the Julia package QuadGK.jl [4] (which can compute Gauss–Kronrod formulas to arbitrary precision).
LibreOffice Calc is the spreadsheet component of the LibreOffice software package. [6] [7]After forking from OpenOffice.org in 2010, LibreOffice Calc underwent a massive re-work of external reference handling to fix many defects in formula calculations involving external references, and to boost data caching performance, especially when referencing large data ranges.