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Discretization is also related to discrete mathematics, and is an important component of granular computing. In this context, discretization may also refer to modification of variable or category granularity, as when multiple discrete variables are aggregated or multiple discrete categories fused.
Typically data is discretized into partitions of K equal lengths/width (equal intervals) or K% of the total data (equal frequencies). [1] Mechanisms for discretizing continuous data include Fayyad & Irani's MDL method, [2] which uses mutual information to recursively define the best bins, CAIM, CACC, Ameva, and many others [3]
In applied mathematics, the non-uniform discrete Fourier transform (NUDFT or NDFT) of a signal is a type of Fourier transform, related to a discrete Fourier transform or discrete-time Fourier transform, but in which the input signal is not sampled at equally spaced points or frequencies (or both).
In discrete modelling, discrete formulae are fit to data. A common method in this form of modelling is to use recurrence relation. Discretization concerns the process of transferring continuous models and equations into discrete counterparts, often for the purposes of making calculations easier by using approximations.
It is a Riemann-solver-free, second-order, high-resolution scheme that uses MUSCL reconstruction. It is a fully discrete method that is straight forward to implement and can be used on scalar and vector problems, and can be viewed as a Rusanov flux (also called the local Lax-Friedrichs flux) supplemented with high order reconstructions.
Method of lines - the example, which shows the origin of the name of method. The method of lines (MOL, NMOL, NUMOL [1] [2] [3]) is a technique for solving partial differential equations (PDEs) in which all but one dimension is discretized.
More precisely, the GDM starts by defining a Gradient Discretization (GD), which is a triplet = (,,,), where: the set of discrete unknowns X D , 0 {\displaystyle X_{D,0}} is a finite dimensional real vector space,
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