Extensions of the first and second complex-step derivative approximations

Journal of Computational and Applied Mathematics

Volumn 219, Issue 1, 2008, Pages 276-293

  Lai, K L ^a   Crassidis, J L ^a  

^a State University of New York   (United States)

Author keywords

Complex step; Finite difference; Hessian; Jacobian

Indexed keywords

APPROXIMATION THEORY; DIFFRACTIVE OPTICAL ELEMENTS; ERRORS; NUMERICAL ANALYSIS; STANDARDS;

ELSEVIER (CO); FINITE DIFFERENCE (FD); FIRST DERIVATIVES; GENERAL (CO); GENERAL FRAMEWORK; NUMERICAL DERIVATIVES; OPTIMAL ACCURACY; ROUND-OFF ERRORS; SECOND DERIVATIVES; STEP SIZE; WIDER RANGE;

DERIVATIVES;

EID: 45249107990     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2007.07.026     Document Type: Article

References (10)

1. Cerviño L.I., and Bewley T.R. On the extension of the complex-step derivative technique to pseudospectral algorithms. J. Comput. Phys. 187 (2003) 544-549
2. J. Kim, D.G. Bates, I. Postlethwaite, Complex-step gradient approximation for robustness analysis of nonlinear systems, in: Proceedings of the IFAC World Congress on Automatic Control, Prague, 2005.
3. K.-L. Lai, Generalizations of the complex-step derivative approximation, Ph.D. thesis, University at Buffalo, State University of New York, NY, Buffalo, NY, September 2006.
4. J.N. Lyness, Numerical algorithms based on the theory of complex variable, in: Proceedings-ACM National Meeting, 1967, pp. 125-133.
5. Lyness J.N., and Moler C.B. Numerical differentiation of analytic functions. SIAM J. Numer. Anal. 4 (1967) 202-210
6. J.R.R.A. Martins, I.M. Kroo, J.J. Alonso, An automated method for sensitivity analysis using complex variables, in: American Institute of Aeronautics and Astronautics, 2000, AIAA-2000-0689.
7. J.R.R.A. Martins, P. Sturdza, J.J. Alonso, The connection between the complex-step derivative approximation and algorithmic differentiation, AIAA Paper 2001-0921, January 2001.
8. Martins J.R.R.A., Sturdza P., and Alonso J.J. The complex-step derivative approximation. ACM Trans. Math. Software 29 (2003) 245-262
9. C. Pozrikidis, Numerical Computation in Science and Engineering, Oxford University Press, New York, NY, 1998, pp. 45-47 (Chapter 1).
10. Squire W., and Trapp G. Using complex variables to estimate derivatives of read functions. SIAM Rev. 40 (1998) 110-112