NumericGradRichardson Routine

Summary

Numerical gradient by high precision numerical differentiation.

Declaration

Procedure NumericGradRichardson(Fun: TRealFunction; Pars: TVec; const Consts: array of TSample; const ObjConst: array of TObject; Grad: TVec);

Parameter	Description
Fun	Real function of several variables.
Pars	Function variables.
Consts	Array of additional constants which can be used in math formula.
PConsts	Array of additional constants (pointers) which can be used in math formula.
Grad	Returns calculated gradient. If needed, Grad Length and Complex properties are adjusted automatically.

Description

Calculates the numerical gradient by high precision numerical differentiation. The algorithm uses Richardson extrapolation of three values of the symmetric difference quotient. The gradient step size is defined by GradStepSize global variable. Normally the optimal stepsize depends on seventh partial derivatives of the function. Since they are not available, the initial value for GradientStepSize is:

Exp(Ln(EPS)/7)*0.25,

as suggested by Spellucci.

See Also
NumericGradDifference
BFGS
ConjGrad
TGrad