Bibliography¶
- DErrico06
J. R. D'Errico. Adaptive robust numerical differentiation. http://www.mathworks.com/matlabcentral/fileexchange/13490-adaptive-robust-numerical-differentiation, 2006.
- For81
B. Fornberg. Numerical differentiation of analytic functions. ACM Transactions on Mathematical Software (TOMS), 7(4):512–526, 1981.
- For98
B. Fornberg. Calculation of weights_and_points in finite difference formulas. SIAM Review, 40:685–691, 1998.
- GLD12
R.P. Russell Gregory Lantoine and T. Dargent. Using multicomplex variables for automatic computation of high-order derivatives. ACM Transactions on Mathematical Software, 2012.
- Gro18
Numerical Algorithms Group. Nag fortran library document: d04aaf. https://www.nag.com/numeric/fl/nagdoc_latest/html/d04/d04aaf.html, 2018.
- JML66
C. B. Moler J. M. Lyness. Vandermonde systems and numerical differentiation. Numerische Mathematik, 8:458–464, 1966.
- JML69
C. B. Moler J. M. Lyness. Generalized romberg methods for integrals of derivatives. Numerische Mathematik, 14:1–14, 1969.
- JPerktold14
J.Perktold. Numdiff package. http://statsmodels.sourceforge.net/0.6.0/_modules/statsmodels/tools/numdiff.html, 2014.
- KLLK05
Y. Cheng K.-L. Lai, J.L. Crassidis and J. Kim. New complex step derivative approximations with application to second-order kalman filtering. AIAA Guidance, Navigation and Control Conference, San Francisco, California, August 2005, AIAA-2005-5944, 2005.
- Lan10
Gregory Lantoine. A methodology for robust optimization of low-thrust trajectories in multi-body environments. PhD thesis, Georgia Institute of Technology, 2010.
- MELEV12
D.C. Struppa M.E. Luna-Elizarraras, M. Shapiro and A. Vajiac. Bicomplex numbers and their elementary functions. CUBO A Mathematical Journal, 14(2):61–68, 2012.
- Rid09
M.S. Ridout. Statistical applications of the complex-step method of numerical differentiation. The American Statistician, 63:66–74, 2009.
- Ver14
Adriaen Verheyleweghen. Computation of higher-order derivatives using the multi-complex step method. Project report, NTNU, Trondheim, Norway, 2014.