Package com.imsl.test.example.math

Class NumericalDerivativesEx3

java.lang.Object

com.imsl.test.example.math.NumericalDerivativesEx3

public class NumericalDerivativesEx3
extends Object

Approximates the gradient with a combination of numerical derivatives and analytic derivatives.

This example uses the same data as in NumericalDerivativesEx2. An examination of the function $$f(y_1 ,y_2 ) = a\exp (by_1 ) + cy_1 y_2^2$$ shows that the first term on the right-hand side does not depend on the second variable, and therefore can be left out of the evaluation of the first partial of \( f \) with respect to \( y_2 \), potentially avoiding cancellation errors. Also, \( cy_2^2 \) appears as an additive term when computing the partial with respect to \(y_1\). This examples shows how different terms in a derivative can be used explicitly and then added to approximated terms. The input values of array options allow NumericalDerivatives to use these facts and obtain greater accuracy using fewer evaluations of the exponential function.

See Also:

• Code
• Output

Constructor Summary

Constructors

Constructor	Description
NumericalDerivativesEx3()

Method Summary

Modifier and Type	Method	Description
static void	main(String[] args)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

NumericalDerivativesEx3

public NumericalDerivativesEx3()

Method Details

main

public static void main(String[] args)