Linear operator

linear operator

1. A mathematical operator that involves only a linear combination of terms or differentials in the dependent variable; examples are the del operator, the Laplacian operator, and the differential operator, L where

   

   the coefficients a₁(x) · · · a_n(x) may be functions of the independent variable x.

   
   
2. A weighting function that is applied to past values of a time series in order to obtain estimates of future values, determined mathematically in such a way that the mean-square error of prediction is minimized.

   
   

   This technique can be extended to more than one variable, so that many time series may be considered simultaneously.

   
   

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