Directions for computing truncated multivariate Taylor series

DOI10.1090/S0025-5718-04-01657-6zbMath1052.65012MaRDI QIDQ4821051

Richard D. Neidinger

Publication date: 7 October 2004

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

zbMATH Keywords

algorithmautomatic differentiationNewton formdivided differencehigh-order derivativesmultivariate polynomial interpolationmultivariate Taylor coefficients

Mathematics Subject Classification ID

Numerical interpolation (65D05) Multidimensional problems (41A63) Interpolation in approximation theory (41A05) Numerical differentiation (65D25) Complexity and performance of numerical algorithms (65Y20)

Related Items (11)

Approximation of solutions of polynomial partial differential equations in two independent variables ⋮ Solving the stationary Navier-Stokes equations by using Taylor meshless method ⋮ A Taylor series method for the solution of the linear initial-boundary-value problems for partial differential equations ⋮ Taylor meshless method for solving non-linear partial differential equations ⋮ Computing the region of convergence for power series in many real variables: A ratio-like test ⋮ Automatic implementation of the numerical Taylor series method: a \textsc{Mathematica} and \textsc{Sage} approach ⋮ Comparing high-order multivariate AD methods ⋮ Convergence analysis and adaptive strategy for the certified quadrature over a set defined by inequalities ⋮ Changing variables in Taylor series with applications to PDEs ⋮ Multivariate Polynomial Interpolation in Newton Forms ⋮ Adaptive Hamiltonian Variational Integrators and Applications to Symplectic Accelerated Optimization

Uses Software

• FFADlib

Cites Work

• Automatic differentiation of functions of many variables
• Computational aspects of multivariate polynomial interpolation
• Polynomial interpolation in several variables
• An efficient method for the numerical evaluation of partial derivatives of arbitrary order
• Data structure and algorithms for fast automatic differentiation
• On Multivariate Lagrange Interpolation
• Evaluating higher derivative tensors by forward propagation of univariate Taylor series
• Some observations on interpolation in higher dimensions
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