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2.4.1 Derivative Programming     continued...

The output consists of a series of values for RATIO (ratio of old to new errors) printed for each until the truncation error and/or is very small. If RATIO tends to 4 as is decreased (and the error is relatively small) the gradient is correct, and if RATIO tends to 8 both the gradient and Hessian are correct. If RATIO tends to 2, which is , neither the gradient nor the Hessian are correct. If RATIO tends to unity, the errors may be too large given the perturbation vector . Thus in general, reliable values of RATIO should occur when: (1) is not too large and not too small, and (2) the difference between and the Taylor-series approximation is of reasonable magnitude. Different starting point and/or perturbation vectors can be tried for verification. The code for TESTGH can be found in file testgh.f in connection with the online version of this paper. To view this file, click on testgh.f.