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ExtremumCurvature Property
Gets the curvature at the extremum.

Namespace:  Meta.Numerics.Analysis
Assembly:  Meta.Numerics (in Meta.Numerics.dll) Version: 3.1.0.0 (3.1.0.0)
Syntax
public double Curvature { get; }

Property Value

Type: Double
Remarks

The curvature is the second derivative of the function at the extremum.

At a typical extremum, where the function has vanishing first derivative, the second derivative will be a number whose magnitude characterizes the "steepness" with which the function increases as one moves away from the extremum.

At an atypical extremum, for example at an interval boundary or of a non-smooth function, this value may be meaningless.

Even in the case of a typical extremum, the value of the curvature property will typically be accurate only to a handfull of digits. If you require a highly accurate determination of the curvature, you should compute the second derivative of the minimzed function explicitly.

See Also