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A note on the computational complexity of chain rule differentiation.

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Title: A note on the computational complexity of chain rule differentiation.
Authors: Naumann, U.1 (AUTHOR) naumann@stce.rwth-aachen.de
Source: Optimization Methods & Software. Apr2026, Vol. 41 Issue 2, p386-393. 8p.
Subjects: NP-complete problems, Jacobian matrices, Floating-point arithmetic, Differentiation (Mathematics), Computational complexity
Abstract: We generalize the proof of NP-completeness of Jacobian accumulation using a given number of floating-point operations to arbitrary order. [ABSTRACT FROM AUTHOR]
Copyright of Optimization Methods & Software is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="DE" term="%22NP-complete+problems%22">NP-complete problems</searchLink><br /><searchLink fieldCode="DE" term="%22Jacobian+matrices%22">Jacobian matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Floating-point+arithmetic%22">Floating-point arithmetic</searchLink><br /><searchLink fieldCode="DE" term="%22Differentiation+%28Mathematics%29%22">Differentiation (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+complexity%22">Computational complexity</searchLink>
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  Data: We generalize the proof of NP-completeness of Jacobian accumulation using a given number of floating-point operations to arbitrary order. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Optimization Methods & Software is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1080/10556788.2023.2263809
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      – Code: eng
        Text: English
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        StartPage: 386
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        Type: general
      – SubjectFull: Jacobian matrices
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      – SubjectFull: Floating-point arithmetic
        Type: general
      – SubjectFull: Differentiation (Mathematics)
        Type: general
      – SubjectFull: Computational complexity
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      – TitleFull: A note on the computational complexity of chain rule differentiation.
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              Text: Apr2026
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              Y: 2026
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