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The method can easily be extended to other dimensional spaces and it is in fact a generalization of Lagrange approximation into a multidimensional spaces. A modified version of the algorithm designed for trivariate interpolation was developed by Robert J. Renka [4] and is available in Netlib as algorithm 661 in the TOMS Library.
The difference between the forecast and the observations at that time is called the departure or the innovation (as it provides new information to the data assimilation process). A weighting factor is applied to the innovation to determine how much of a correction should be made to the forecast based on the new information from the observations.
Linear trend estimation is a statistical technique used to analyze data patterns. Data patterns, or trends, occur when the information gathered tends to increase or decrease over time or is influenced by changes in an external factor.
The simplest interpolation method is to locate the nearest data value, and assign the same value. In simple problems, this method is unlikely to be used, as linear interpolation (see below) is almost as easy, but in higher-dimensional multivariate interpolation, this could be a favourable choice for its speed and simplicity.
Exponential smoothing or exponential moving average (EMA) is a rule of thumb technique for smoothing time series data using the exponential window function.Whereas in the simple moving average the past observations are weighted equally, exponential functions are used to assign exponentially decreasing weights over time.
In statistics, best linear unbiased prediction (BLUP) is used in linear mixed models for the estimation of random effects.BLUP was derived by Charles Roy Henderson in 1950 but the term "best linear unbiased predictor" (or "prediction") seems not to have been used until 1962. [1] "
Nearest-neighbor interpolation (also known as proximal interpolation or, in some contexts, point sampling) is a simple method of multivariate interpolation in one or more dimensions. Interpolation is the problem of approximating the value of a function for a non-given point in some space when given the value of that function in points around ...
Time series forecasting is the use of a model to predict future values based on previously observed values. Generally, time series data is modelled as a stochastic process .
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