Accurate Numerical Derivatives
Calculate (accurate) numerical approximations to derivatives.
The main functions are
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.
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.