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Automatic Differentiation: Introduction, History and Rounding Error Estimation

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Encyclopedia of Optimization
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Article Outline

Keywords

Introduction

  Algorithms

  Complexity

History

Estimates of Rounding Errors

See also

References

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References

  1. Baur W, Strassen V (1983) The complexity of partial derivatives. Theor Comput Sci 22:317–330

    MathSciNet  MATH  Google Scholar 

  2. Berz M, Bischof C, Corliss G, Griewank A (eds) (1996) Computational differentiation: Techniques, applications, and tools. SIAM, Philadelphia

    MATH  Google Scholar 

  3. Griewank A (1992) Achieving logarithmic growth of temporal and spatial complexity in reverse automatic differentiation. Optim Methods Soft 1:35–54

    Google Scholar 

  4. Griewank A, Corliss GF (eds) (1991) Automatic differentiation of algorithms: Theory, implementation, and application. SIAM, Philadelphia

    MATH  Google Scholar 

  5. Hillstrom KE (1985) Installation guide for JAKEF. Techn Memorandum Math and Computer Sci Div Argonne Nat Lab ANL/MCS-TM-17

    Google Scholar 

  6. Hillstrom KE (1985) User guide for JAKEF. Techn Memorandum Math and Computer Sci Div Argonne Nat Lab ANL/MCS-TM-16

    Google Scholar 

  7. Iri M (1984) Simultaneous computation of functions, partial derivatives and estimates of rounding errors – Complexity and practicality. Japan J Appl Math 1:223–252

    MathSciNet  MATH  Google Scholar 

  8. Iri M, Tsuchiya T, Hoshi M (1988) Automatic computation of partial derivatives and rounding error estimates with applications to large-scale systems of nonlinear equations. J Comput Appl Math 24:365–392

    MATH  Google Scholar 

  9. Kagiwada H, Kalaba R, Rasakhoo N, Spingarn K (1986) Numerical derivatives and nonlinear analysis. Math. Concepts and Methods in Sci. and Engin., vol 31. Plenum, New York

    MATH  Google Scholar 

  10. Kubota K, Iri M (1991) Estimates of rounding errors with fast automatic differentiation and interval analysis. J Inform Process 14:508–515

    MathSciNet  MATH  Google Scholar 

  11. Linnainmaa S (1976) Taylor expansion of the accumulated rounding error. BIT 16:146–160

    MathSciNet  MATH  Google Scholar 

  12. Miller W, Wrathall C (1980) Software for roundoff analysis of matrix algorithms. Acad Press, New York

    MATH  Google Scholar 

  13. Ostrovskii GM, Wolin JM, Borisov WW (1971) Über die Berechnung von Ableitungen. Wiss Z Techn Hochschule Chemie 13:382–384

    Google Scholar 

  14. Rall LB (1981) Automatic differentiation – Techniques and applications. Lecture Notes Computer Science, vol 120. Springer, Berlin

    MATH  Google Scholar 

  15. Speelpenning B (1980) Compiling fast partial derivatives of functions given by algorithms. Report Dept Computer Sci Univ Illinois UIUCDCS-R-80-1002

    Google Scholar 

  16. Wengert RE (1964) A simple automatic derivative evaluation program. Comm ACM 7:463–464

    MATH  Google Scholar 

  17. Werbos P (1974) Beyond regression: New tools for prediction and analysis in the behavioral sciences. PhD Thesis, Appl. Math. Harvard University

    Google Scholar 

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© 2008 Springer-Verlag

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Iri, M., Kubota, K. (2008). Automatic Differentiation: Introduction, History and Rounding Error Estimation . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_26

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