Evaluating higher derivative tensors by forward propagation of univariate Taylor series

DOI10.1090/S0025-5718-00-01120-0zbMath0952.65028OpenAlexW1992493944WikidataQ57389664 ScholiaQ57389664MaRDI QIDQ4955864

Andrea Walther, Jean Utke, Andreas Griewank

Publication date: 22 May 2000

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-00-01120-0

zbMATH Keywords

partial derivativeshigher order derivativestensorsfunction of several variablescomputational complexitiescomputational differentiation

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Numerical differentiation (65D25) Complexity and performance of numerical algorithms (65Y20) Numerical methods in Fourier analysis (65T99)

Related Items

On higher-order differentiation in nonlinear mechanics, On evaluating higher-order derivatives of the QR decomposition of tall matrices with full column rank in forward and reverse mode algorithmic differentiation, Solving the stationary Navier-Stokes equations by using Taylor meshless method, Sensitivity analysis with finite changes: an application to modified EOQ models, Directions for computing truncated multivariate Taylor series, Computing of B-series by automatic differentiation, On the efficient computation of high-order derivatives for implicitly defined functions, On the numerical stability of algorithmic differentiation, Taylor meshless method for solving non-linear partial differential equations, Automatic implementation of the numerical Taylor series method: a \textsc{Mathematica} and \textsc{Sage} approach, Computation of multiple Lie derivatives by algorithmic differentiation, TaylUR, an arbitrary-order diagonal automatic differentiation package for Fortran 95, Validated computation of the local truncation error of Runge–Kutta methods with automatic differentiation, Arbogast: Higher order automatic differentiation for special functions with Modular C, Comparing high-order multivariate AD methods, Unnamed Item, Convergence analysis and adaptive strategy for the certified quadrature over a set defined by inequalities, Higher-order reverse automatic differentiation with emphasis on the third-order, Sensitivity computations in higher order continuation methods, Changing variables in Taylor series with applications to PDEs, Higher order Langevin Monte Carlo algorithm, Automatic evaluations of cross-derivatives, Maximum Likelihood Estimation for a Smooth Gaussian Random Field Model

Uses Software

• ADOL-C

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Computation of cusp singularities for operator equations and their discretizations
• Bifurcation and chaos: Analysis, algorithms, applications. Proceedings of a conference held in Würzburg/Germany, August 20-24, 1990
• Algorithm 755: ADOL-C
• An efficient method for the numerical evaluation of partial derivatives of arbitrary order