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In linear algebra and numerical analysis, a preconditioner of a matrix is a matrix such that has a smaller condition number than .It is also common to call = the preconditioner, rather than , since itself is rarely explicitly available.
Condition numbers can also be defined for nonlinear functions, and can be computed using calculus.The condition number varies with the point; in some cases one can use the maximum (or supremum) condition number over the domain of the function or domain of the question as an overall condition number, while in other cases the condition number at a particular point is of more interest.
In probability theory and statistics, a conditional variance is the variance of a random variable given the value(s) of one or more other variables. Particularly in econometrics, the conditional variance is also known as the scedastic function or skedastic function. [1]
On the discrete level, conditioning is possible only if the condition is of nonzero probability (one cannot divide by zero). On the level of densities, conditioning on X = x is possible even though P ( X = x) = 0. This success may create the illusion that conditioning is always possible. Regretfully, it is not, for several reasons presented below.
The red line represents the local polynomial being used to fit a sub-set of the data. The smoothed values are shown as circles. A Savitzky–Golay filter is a digital filter that can be applied to a set of digital data points for the purpose of smoothing the data, that is, to increase the precision of the data without distorting the signal ...
Conditioning on a continuous random variable is not the same as conditioning on the event {=} as it was in the discrete case. For a discussion, see Conditioning on an event of probability zero . Not respecting this distinction can lead to contradictory conclusions as illustrated by the Borel-Kolmogorov paradox .
The second smallest eigenvalue of L (could be zero) is the algebraic connectivity (or Fiedler value) of G and approximates the sparsest cut of a graph. The Laplacian is an operator on the n-dimensional vector space of functions f : V → R {\textstyle f:V\to \mathbb {R} } , where V {\textstyle V} is the vertex set of G, and n = | V ...
The different steps of the data analysis process are carried out in order to realise smart buildings, where the building management and control operations including heating, ventilation, air conditioning, lighting and security are realised automatically by miming the needs of the building users and optimising resources like energy and time.