Complexity of Gradients, Jacobians, and Hessians

Griewank, Andreas

doi:10.1007/978-0-387-74759-0_78

Complexity of Gradients, Jacobians, and Hessians

SA

Andreas Griewank³

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Article Outline

Keywords

‘Numerical’ Differentiation Methods

‘Analytical’ Differentiation Methods

Two-Stranded Chain Scenario

Computational Model

Indefinite Integral Scenario

Lack of Smoothness

Predictability of Complexities

Goal-Oriented Differentiation

The Computational Graph

Forward Mode

Bauer's Formula

Reverse Mode

Second Order Adjoints

Overheads

Worst-Case Optimality

Expensive ≡ Redundant?

Preaccumulation and Combinatorics

Summary

References

Bauer FL (1974) Computational graphs and rounding error. SIAM J Numer Anal 11:87–96
Article MATH MathSciNet Google Scholar
Berz M, Bischof Ch, Corliss G, Griewank A (eds) (1996) Computational differentiation: Techniques, applications, and tools. SIAM, Philadelphia
MATH Google Scholar
Bischof Ch, Carle A, Corliss G, Griewank A, Hovland P (1992) ADIFOR: Generating derivative codes from Fortran programs. Scientif Program 1:1–29
Google Scholar
Coleman TF, Morée JJ (1984) Estimation of sparse Jacobian matrices and graph coloring problems. SIAM J Numer Anal 20:187–209
Article MathSciNet Google Scholar
Coleman TF, Verma A (1996) Structure and efficient Jacobian calculation. In: Berz M, Bischof Ch, Corliss G, Griewank A (eds) Computational Differentiation: Techniques, Applications, and Tools. SIAM, Philadelphia, pp 149–159
Google Scholar
Curtis AR, Powell MJD, Reid JK (1974) On the estimation of sparse Jacobian matrices. J Inst Math Appl 13:117–119
MATH Google Scholar
Griewank A (1991) The chain rule revisited in scientific computing, I–II. SIAM News
Google Scholar
Griewank A (1992) Achieving logarithmic growth of temporal and spatial complexity in reverse automatic differentiation. Optim Methods Softw 1:35–54
Article Google Scholar
Griewank A (2000) Evaluating derivatives, principles and techniques of algorithmic differentiation. Frontiers in Appl Math, vol 19. SIAM, Philadelphia
MATH Google Scholar
Griewank A, Corliss GF (eds) (1991) Automatic differentiation of algorithms: Theory, implementation, and application. SIAM, Philadelphia
MATH Google Scholar
Griewank A, Reese S (1991) On the calculation of Jacobian matrices by the Markowitz rule. In: Griewank A and Corliss GF (eds) Automatic Differentiation of Algorithms: Theory, Implementation, and Application. SIAM, Philadelphia, pp 126–135
Google Scholar
Newsam GN, Ramsdell JD (1983) Estimation of sparse Jacobian matrices. SIAM J Alg Discrete Meth 4:404–417
Article MATH MathSciNet Google Scholar

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Authors and Affiliations

Institute Sci. Comput. Department Math., Techn. University Dresden, Dresden, Germany
Andreas Griewank

Authors

Andreas Griewank
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Editor information

Editors and Affiliations

Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544-5263, USA
Christodoulos A. Floudas
Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611-6595, USA
Panos M. Pardalos

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Griewank, A. (2008). Complexity of Gradients, Jacobians, and Hessians . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_78

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DOI: https://doi.org/10.1007/978-0-387-74759-0_78
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-74758-3
Online ISBN: 978-0-387-74759-0
eBook Packages: Mathematics and StatisticsReference Module Computer Science and Engineering

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