The Efficient Computation of Structured Gradients using Automatic Differentiation

Autor:	Gudbjorn F. Jonsson, Thomas F. Coleman
Rok vydání:	1999
Předmět:	Implicit function Automatic differentiation Applied Mathematics Computation Function (mathematics) Inverse problem Computational Mathematics symbols.namesake Dimension (vector space) Jacobian matrix and determinant symbols Time complexity Algorithm Mathematics
Zdroj:	SIAM Journal on Scientific Computing. 20:1430-1437
ISSN:	1095-7197 1064-8275
DOI:	10.1137/s1064827597320794
Popis:	The advent of robust automatic differentiation tools is an exciting and important development in scientific computing. It is particularly noteworthy that the gradient of a scalar-valued function of many variables can be computed with essentially the same time complexity as required to evaluate the function itself. This is true, in theory, when the "reverse mode" of automatic differentiation is used (whereas the "forward mode" introduces an additional factor corresponding to the problem dimension). However, in practice, performance on large problems can be significantly (and unacceptably) worse than predicted. In this paper we illustrate that when natural structure is exploited, fast gradient computation can be recovered, even for large dimensional problems.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::1324e53a394b4ebbddf5afc85e12af5d https://doi.org/10.1137/s1064827597320794 Zobrazit plný text záznamu Plný text ve formátu PDF