Thus, the error function is quadratic with respect to the parameter vector and can be differentiated easily to a linear system.
22.
The filter design process can be described as an optimization problem where each requirement contributes to an error function which should be minimized.
23.
Once the error function is established, the optimal filter is given by the coefficients f ( x ) which minimize \ varepsilon.
24.
The same integral with finite limits is closely related both to the error function and the cumulative distribution function of the normal distribution.
25.
A simple example of a function without a closed form antiderivative is, whose antiderivative is ( up to constants ) the error function.
26.
Gaussian functions are among those functions that are elementary but lack elementary antiderivatives; the integral of the Gaussian function is the error function.
27.
The most famous such example is the error function, which is related to the cumulative distribution function ( CDF ) of a normal distribution.
28.
It is an iterative algorithm that converges to a polynomial that has an error function with " N " + 2 level extrema.
29.
From this, solutions of arbitrarily high accuracy may be developed based on Steinbrecher's approach to the series for the inverse error function.
30.
All generalised error functions for " n " > 0 look similar on the positive " x " side of the graph.
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