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Automation of Nested Matrix and Derivative Operations


  • Kalaba, Robert E.
  • Plum, Thomas
  • Tesfatsion, Leigh S.


In Kalaba, Tesfatsion, and Wang (JMAA,1983) an algorithm was developed for the exact forward-mode automatic evaluation of higher-order partial derivatives of functions of many variables using derivative arrays. This algorithm was supported by a library of "calculus subroutines" for many standard one-variable and two-variable functions. This article extends the FEED library to permit the automatic differentiation of expressions involving nested matrix and derivative operations. The need to differentiate such expressions arose naturally in the course of designing sequential filters for a class of nonlinear tracking problems. Annotated pointers to related work can be accessed at:

Suggested Citation

  • Kalaba, Robert E. & Plum, Thomas & Tesfatsion, Leigh S., 1987. "Automation of Nested Matrix and Derivative Operations," Staff General Research Papers Archive 11202, Iowa State University, Department of Economics.
  • Handle: RePEc:isu:genres:11202

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    Cited by:

    1. Max E. Jerrell, "undated". "Automatic Differentiation and Interval Arithmetic for Estimation of Disequilibrium Models," Computing in Economics and Finance 1996 _028, Society for Computational Economics.
    2. Max E. Jerrell, 1999. "Environments for Global Optimization Using Interval Arithmetic and Computational (Automatic) Differentiation," Computing in Economics and Finance 1999 1321, Society for Computational Economics.

    More about this item


    automatic differentiation; nested matrix and derivative operations; FEED library;

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling


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