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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 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.
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 ...
Throughout this article, boldfaced unsubscripted and are used to refer to random vectors, and Roman subscripted and are used to refer to scalar random variables.. If the entries in the column vector = (,, …,) are random variables, each with finite variance and expected value, then the covariance matrix is the matrix whose (,) entry is the covariance [1]: 177 ...
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 .
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.