Linear operator: Difference between revisions
From Glossary of Meteorology
(Created page with " {{TermHeader}} {{TermSearch}} <div class="termentry"> <div class="term"> == linear operator == </div> #<div class="definition"><div class="short_definition">A mathemat...") |
m (Rewrite with Template:Term and clean up) |
||
| Line 1: | Line 1: | ||
{{Term | |||
|Display title=linear operator | |||
{{ | |Definitions={{Definition | ||
{{ | |Num=1 | ||
|Meaning= | |||
#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 <blockquote>[[File:ams2001glos-Le21.gif|link=|center|ams2001glos-Le21]]</blockquote> the coefficients ''a''<sub>1</sub>(''x'') · · · ''a''<sub>''n''</sub>(''x'') may be functions of the [[independent variable]] ''x''.<br/> | |||
#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.<br/> This technique can be extended to more than one [[variable]], so that many time series may be considered simultaneously. | |||
}} | |||
}} | |||
# | |||
# | |||
Latest revision as of 05:49, 29 March 2024
- 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) · · · an(x) may be functions of the independent variable x.
- 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.
