Description Details Author(s) References

Calculate (accurate) numerical approximations to derivatives.

The main functions are

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
grad to calculate the gradient (first derivative) of a scalar
real valued function (possibly applied to all elements
of a vector argument).
jacobian to calculate the gradient of a real m-vector valued
function with real n-vector argument.
hessian to calculate the Hessian (second derivative) of a scalar
real valued function with real n-vector argument.
genD to calculate the gradient and second derivative of a
real m-vector valued function with real n-vector
argument.
``` |

Paul Gilbert, based on work by Xingqiao Liu, and Ravi Varadhan (who wrote complex-step derivative codes)

Linfield, G. R. and Penny, J. E. T. (1989) *Microcomputers in Numerical
Analysis*. New York: Halsted Press.

Fornberg, B. and Sloan, D, M. (1994) “A review of pseudospectral methods
for solving partial differential equations.” *Acta Numerica*, 3, 203-267.

Lyness, J. N. and Moler, C. B. (1967) “Numerical Differentiation of Analytic
Functions.” *SIAM Journal for Numerical Analysis*,
4(2), 202-210.

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