Automatic computation of partial derivatives and rounding error estimates with applications to large-scale systems of nonlinear equations

DOI10.1016/0377-0427(88)90298-1zbMath0677.65015OpenAlexW2064643369MaRDI QIDQ1123531

Masao Iri, Takashi Tsuchiya, Mamoru Hoshi

Publication date: 1988

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(88)90298-1

zbMATH Keywords

algorithmJacobianerror estimateslarge-scale systemsnumerical differentiationautomatic computationrounding errorspartial derivatives

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Numerical differentiation (65D25) Computer aspects of numerical algorithms (65Yxx)

Related Items (6)

Matrix inversion algorithms by means of automatic differentiation ⋮ Algorithmic differentiation for adjoint sensitivity calculation in plasma edge codes ⋮ On the numerical stability of algorithmic differentiation ⋮ Automatic differentiation of the vector that solves a parametric linear system ⋮ Sum of uniformly distributed random variables and a family of nonalyticC ∞-functions ⋮ On operators defining a family of nonanalyticC ∞-functions

Cites Work

• Automatic differentiation: techniques and applications
• The complexity of partial derivatives
• First Partial Differentiation by Computer with an Application to Categorical Data Analysis
• Simultaneous computation of functions, partial derivatives and estimates of rounding errors —Complexity and practicality—
• Computational Graphs and Rounding Error
• A simple automatic derivative evaluation program
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