mean square deviation

If f is a Riemann integrablePlanetmathPlanetmath real function on the interval[a,b] which is wished to be approximated by another functionMathworldPlanetmath φ with the same property, then the mean (


is called the mean square deviation of φ from f.

For example, if  sinx  is approximated by x on  [0,π2], the mean square deviation is

2π0π2(sinx-x)2𝑑x 0.04923.
Title mean square deviation
Canonical name MeanSquareDeviation
Date of creation 2013-03-22 18:21:57
Last modified on 2013-03-22 18:21:57
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 8
Author pahio (2872)
Entry type Definition
Classification msc 26A06
Classification msc 41A99
Classification msc 26A42
Synonym mean squared error
Related topic Variance
Related topic RmsError
Related topic AverageValueOfFunction