Yang, Jie; Koutsawa, Yao; Potier-Ferry, Michel; Hu, Heng Changing variables in Taylor series with applications to PDEs. (English) Zbl 07165905 Eng. Anal. Bound. Elem. 112, 77-86 (2020). MSC: 65 35 PDF BibTeX XML Cite \textit{J. Yang} et al., Eng. Anal. Bound. Elem. 112, 77--86 (2020; Zbl 07165905) Full Text: DOI
Sabanis, Sotirios; Zhang, Ying Higher order Langevin Monte Carlo algorithm. (English) Zbl 1429.60006 Electron. J. Stat. 13, No. 2, 3805-3850 (2019). MSC: 60-08 60H10 65C05 PDF BibTeX XML Cite \textit{S. Sabanis} and \textit{Y. Zhang}, Electron. J. Stat. 13, No. 2, 3805--3850 (2019; Zbl 1429.60006) Full Text: DOI Euclid arXiv
Yang, Jie; Potier-Ferry, Michel; Hu, Heng Solving the stationary Navier-Stokes equations by using Taylor meshless method. (English) Zbl 1404.76197 Eng. Anal. Bound. Elem. 98, 8-16 (2019). MSC: 76M25 65N99 76D05 PDF BibTeX XML Cite \textit{J. Yang} et al., Eng. Anal. Bound. Elem. 98, 8--16 (2019; Zbl 1404.76197) Full Text: DOI
Neidinger, Richard D.; Altman, Benjamin Comparing high-order multivariate AD methods. (English) Zbl 1401.65026 Optim. Methods Softw. 33, No. 4-6, 995-1009 (2018). MSC: 65D25 65Y20 65D05 41A63 41A05 PDF BibTeX XML Cite \textit{R. D. Neidinger} and \textit{B. Altman}, Optim. Methods Softw. 33, No. 4--6, 995--1009 (2018; Zbl 1401.65026) Full Text: DOI
Charpentier, Isabelle; Gustedt, Jens Arbogast: higher order automatic differentiation for special functions with Modular C. (English) Zbl 1455.65006 Optim. Methods Softw. 33, No. 4-6, 963-987 (2018). MSC: 65-04 65D25 68W30 PDF BibTeX XML Cite \textit{I. Charpentier} and \textit{J. Gustedt}, Optim. Methods Softw. 33, No. 4--6, 963--987 (2018; Zbl 1455.65006) Full Text: DOI
Mullier, Olivier; Chapoutot, Alexandre; Alexandre dit Sandretto, Julien Validated computation of the local truncation error of Runge-Kutta methods with automatic differentiation. (English) Zbl 1397.65068 Optim. Methods Softw. 33, No. 4-6, 718-728 (2018). MSC: 65G40 65D30 65L06 65Y20 65L05 65L70 PDF BibTeX XML Cite \textit{O. Mullier} et al., Optim. Methods Softw. 33, No. 4--6, 718--728 (2018; Zbl 1397.65068) Full Text: DOI
Yang, Jie; Hu, Heng; Koutsawa, Yao; Potier-Ferry, Michel Taylor meshless method for solving non-linear partial differential equations. (English) Zbl 1380.65393 J. Comput. Phys. 348, 385-400 (2017). MSC: 65N35 65D25 35J05 65L60 PDF BibTeX XML Cite \textit{J. Yang} et al., J. Comput. Phys. 348, 385--400 (2017; Zbl 1380.65393) Full Text: DOI
Xu, Wanting; Stein, Michael L. Maximum likelihood estimation for a smooth Gaussian random field model. (English) Zbl 06736498 SIAM/ASA J. Uncertain. Quantif. 5, 138-175 (2017). MSC: 62M30 60G15 97N50 PDF BibTeX XML Cite \textit{W. Xu} and \textit{M. L. Stein}, SIAM/ASA J. Uncertain. Quantif. 5, 138--175 (2017; Zbl 06736498) Full Text: DOI
Charpentier, Isabelle; Lampoh, Komlanvi Sensitivity computations in higher order continuation methods. (English) Zbl 1452.35087 Appl. Math. Modelling 40, No. 4, 3365-3380 (2016). MSC: 35K91 35K20 65M06 65P30 PDF BibTeX XML Cite \textit{I. Charpentier} and \textit{K. Lampoh}, Appl. Math. Modelling 40, No. 4, 3365--3380 (2016; Zbl 1452.35087) Full Text: DOI
Gower, R. M.; Gower, A. L. Higher-order reverse automatic differentiation with emphasis on the third-order. (English) Zbl 1332.65034 Math. Program. 155, No. 1-2 (A), 81-103 (2016). MSC: 65D25 15A69 65F50 49Q12 PDF BibTeX XML Cite \textit{R. M. Gower} and \textit{A. L. Gower}, Math. Program. 155, No. 1--2 (A), 81--103 (2016; Zbl 1332.65034) Full Text: DOI arXiv
Abad, A.; Barrio, R.; Marco-Buzunariz, M.; Rodríguez, M. Automatic implementation of the numerical Taylor series method: a Mathematica and Sage approach. (English) Zbl 1410.65243 Appl. Math. Comput. 268, 227-245 (2015). MSC: 65L05 PDF BibTeX XML Cite \textit{A. Abad} et al., Appl. Math. Comput. 268, 227--245 (2015; Zbl 1410.65243) Full Text: DOI
Goldsztejn, Alexandre; Cruz, Jorge; Carvalho, Elsa Convergence analysis and adaptive strategy for the certified quadrature over a set defined by inequalities. (English) Zbl 1293.65036 J. Comput. Appl. Math. 260, 543-560 (2014). MSC: 65D30 65G40 PDF BibTeX XML Cite \textit{A. Goldsztejn} et al., J. Comput. Appl. Math. 260, 543--560 (2014; Zbl 1293.65036) Full Text: DOI
Griewank, Andreas; Lehmann, Lutz; Leovey, Hernan; Zilberman, Marat Automatic evaluations of cross-derivatives. (English) Zbl 1278.65022 Math. Comput. 83, No. 285, 251-274 (2014). MSC: 65D25 68W30 65C05 65T50 91G60 65Y20 PDF BibTeX XML Cite \textit{A. Griewank} et al., Math. Comput. 83, No. 285, 251--274 (2014; Zbl 1278.65022) Full Text: DOI
Bartha, Ferenc A.; Munthe-Kaas, Hans Z. Computing of B-series by automatic differentiation. (English) Zbl 1278.65020 Discrete Contin. Dyn. Syst. 34, No. 3, 903-914 (2014). MSC: 65D25 65L05 65Y20 PDF BibTeX XML Cite \textit{F. A. Bartha} and \textit{H. Z. Munthe-Kaas}, Discrete Contin. Dyn. Syst. 34, No. 3, 903--914 (2014; Zbl 1278.65020) Full Text: DOI
Walter, Sebastian F.; Lehmann, Lutz; Lamour, René On evaluating higher-order derivatives of the QR decomposition of tall matrices with full column rank in forward and reverse mode algorithmic differentiation. (English) Zbl 1242.65048 Optim. Methods Softw. 27, No. 2, 391-403 (2012). MSC: 65D25 12E05 58C15 65F15 65F25 65F05 PDF BibTeX XML Cite \textit{S. F. Walter} et al., Optim. Methods Softw. 27, No. 2, 391--403 (2012; Zbl 1242.65048) Full Text: DOI
Charpentier, I. On higher-order differentiation in nonlinear mechanics. (English) Zbl 1242.41031 Optim. Methods Softw. 27, No. 2, 221-232 (2012). MSC: 41A58 65P30 68N19 74-02 PDF BibTeX XML Cite \textit{I. Charpentier}, Optim. Methods Softw. 27, No. 2, 221--232 (2012; Zbl 1242.41031) Full Text: DOI
Griewank, Andreas; Kulshreshtha, Kshitij; Walther, Andrea On the numerical stability of algorithmic differentiation. (English) Zbl 1238.65013 Computing 94, No. 2-4, 125-149 (2012). MSC: 65D25 65G50 65Y04 PDF BibTeX XML Cite \textit{A. Griewank} et al., Computing 94, No. 2--4, 125--149 (2012; Zbl 1238.65013) Full Text: DOI
Wagner, Mathias; Walther, Andrea; Schaefer, Bernd-Jochen On the efficient computation of high-order derivatives for implicitly defined functions. (English) Zbl 1205.65131 Comput. Phys. Commun. 181, No. 4, 756-764 (2010). MSC: 65D25 81V05 PDF BibTeX XML Cite \textit{M. Wagner} et al., Comput. Phys. Commun. 181, No. 4, 756--764 (2010; Zbl 1205.65131) Full Text: DOI
Borgonovo, E. Sensitivity analysis with finite changes: an application to modified EOQ models. (English) Zbl 1188.90006 Eur. J. Oper. Res. 200, No. 1, 127-138 (2010). MSC: 90B05 90C31 PDF BibTeX XML Cite \textit{E. Borgonovo}, Eur. J. Oper. Res. 200, No. 1, 127--138 (2010; Zbl 1188.90006) Full Text: DOI
Röbenack, Klaus Computation of multiple Lie derivatives by algorithmic differentiation. (English) Zbl 1136.93017 J. Comput. Appl. Math. 213, No. 2, 454-464 (2008). MSC: 93B29 93B40 93C10 PDF BibTeX XML Cite \textit{K. Röbenack}, J. Comput. Appl. Math. 213, No. 2, 454--464 (2008; Zbl 1136.93017) Full Text: DOI
von Hippel, G. M. TaylUR, an arbitrary-order diagonal automatic differentiation package for Fortran 95. (English) Zbl 1196.65216 Comput. Phys. Commun. 174, No. 7, 569-576 (2006). MSC: 65Y99 PDF BibTeX XML Cite \textit{G. M. von Hippel}, Comput. Phys. Commun. 174, No. 7, 569--576 (2006; Zbl 1196.65216) Full Text: DOI
Neidinger, Richard D. Directions for computing truncated multivariate Taylor series. (English) Zbl 1052.65012 Math. Comput. 74, No. 249, 321-340 (2005). MSC: 65D25 65D05 41A05 41A63 65Y20 PDF BibTeX XML Cite \textit{R. D. Neidinger}, Math. Comput. 74, No. 249, 321--340 (2005; Zbl 1052.65012) Full Text: DOI