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Sequential Evaluation of Adjoints and Higher Derivative Vectors by Overloading and Reverse Accumulation.

Please always quote using this URN: urn:nbn:de:0297-zib-539
  • Most nonlinear computations require the evaluation of first and higher derivatives of vector functions defined by computer programs. It is shown here how vectors of such partial derivatives can be obtained automatically and efficiently if the computer language allows overloading (as is or will be the case for C++, PASCAL-XSC, FORTRAN90, and other modern languages). Here, overloading facilitates the extension of arithmetic operations and univariate functions from real or complex arguments to truncated Taylor-series (or other user- defined types), and it generates instructions for the subsequent evaluation of adjoints. Similar effects can be achieved by precompilation of FORTRAN77 programs. The proposed differentiation algorithm yields gradients and higher derivatives at a small multiple of the run-time and RAM requirement of the original function evaluation program. {\bf Keywords:} Automatic Differentiation, Chain Rule, Overloading, Taylor Coefficients, Gradients, Hessians, Reverse Accumulation, Adjoint Equations. {\bf Abbreviated title:} Automatic Differentiation by Overloading.

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Metadaten
Author:Andreas GriewankORCiD
Document Type:ZIB-Report
Tag:Adjoint Equations; Automatic Differentiation; Chain Rule; Gradients; Hessians; Overloading; Reverse Accumulation; Taylor Coefficients
Date of first Publication:1991/05/21
Series (Serial Number):ZIB-Report (SC-91-03)
ZIB-Reportnumber:SC-91-03
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