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Diskr. Mat., 2005, Volume 17, Issue 3, Pages 45–67 (Mi dm115)  

This article is cited in 7 scientific papers (total in 7 papers)

On the complexity of the computation of differentials and gradients

S. B. Gashkov, I. B. Gashkov


Abstract: We obtain bounds for the complexity of circuit realisation of the system of differentials of orders from one to $k$ of an arbitrary elementary function in terms of the circuit complexity of this function. Similar bounds are obtained for the complexities of realisation of the Jacobian and Hessian matrices. We point out some applications to deduction of bounds for complexities of polynomials in several variables, linear transformations, and quadratic forms.
This research was supported by the Russian Foundation for Basic Research, grants 02–01–10142 and 02–01–00985, and by the Program of the President of the Russian Federation for supporting the leading scientific schools, grant 1807.2003.1.

DOI: https://doi.org/10.4213/dm115

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English version:
Discrete Mathematics and Applications, 2005, 15:4, 327–350

Bibliographic databases:

UDC: 519.7
Received: 21.09.2004

Citation: S. B. Gashkov, I. B. Gashkov, “On the complexity of the computation of differentials and gradients”, Diskr. Mat., 17:3 (2005), 45–67; Discrete Math. Appl., 15:4 (2005), 327–350

Citation in format AMSBIB
\Bibitem{GasGas05}
\by S.~B.~Gashkov, I.~B.~Gashkov
\paper On the complexity of the computation of differentials and gradients
\jour Diskr. Mat.
\yr 2005
\vol 17
\issue 3
\pages 45--67
\mathnet{http://mi.mathnet.ru/dm115}
\crossref{https://doi.org/10.4213/dm115}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2195650}
\zmath{https://zbmath.org/?q=an:1082.65027}
\elib{https://elibrary.ru/item.asp?id=9135439}
\transl
\jour Discrete Math. Appl.
\yr 2005
\vol 15
\issue 4
\pages 327--350
\crossref{https://doi.org/10.1515/156939205774464936}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. J. Appl. Industr. Math., 2:3 (2008), 385–396  mathnet  crossref  zmath
    2. S. B. Gashkov, I. S. Sergeev, “A method for deriving lower bounds for the complexity of monotone arithmetic circuits computing real polynomials”, Sb. Math., 203:10 (2012), 1411–1447  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. S. B. Gashkov, “Arithmetic complexity of the Stirling transforms”, Discrete Math. Appl., 25:2 (2015), 83–92  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. S. B. Gashkov, “Arithmetic Complexity of Certain Linear Transformations”, Math. Notes, 97:4 (2015), 531–555  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. Jukna S., “Lower Bounds For Tropical Circuits and Dynamic Programs”, Theor. Comput. Syst., 57:1 (2015), 160–194  crossref  mathscinet  zmath  isi  elib  scopus
    6. S. B. Gashkov, I. S. Sergeev, “On the Additive Complexity of GCD and LCM Matrices”, Math. Notes, 100:2 (2016), 199–212  mathnet  crossref  crossref  mathscinet  isi  elib
    7. Ghosal S.K., Mandal J.K., “On the Use of the Stirling Transform in Image Steganography”, J. Inf. Secur. Appl., 46 (2019), 320–330  crossref  isi
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