Automatic computation of derivatives with the use of the multilevel differentiating technique. I: Algorithmic basis
type: Item
instance of: scholarly article
title: Automatic computation of derivatives with the use of the multilevel differentiating technique. I: Algorithmic basis
zbMATH Open document ID: 0595.65019
DOI: 10.1016/0898-1221(85)90188-9
publication date: 1985-01-01T00:00:00Z
review text: Automatic computation of derivatives plays an important role for the effective solution of diverse computational problems in nonlinear programming, solution of systems of nonlinear equations, etc. For an overview, see \textit{L. B. Rall} [Automatic differentiation: techniques and applications (1981; Zbl 0473.68025)]. Among the approaches used are the so-called forward method (FM) and the backward method (BM), which are based, respectively, on variational and adjoint processes. Both approaches present the differentiated relationship in the form of a computational system whose structure is determined by the oriented computational graph and differ in that the FM computes the derivatives in the sequence answering the graph's orientation while the BM, in the backward sequence. The present paper suggests a differentiation method based upon a multilevel modular unification of FM and BM. With an increased flexibility for accurate differentiation, this method provides in many cases a reasonable compromise between time and memory. The structure of the method is in a good agreement with the conventional modular principle of programming which facilitates its software realization.
Mathematics Subject Classification ID: 65D25
Mathematics Subject Classification ID: 65Yxx
zbMATH DE Number: 3958551
zbMATH Keywords: multilevel differentiating technique
zbMATH Keywords: forward method
zbMATH Keywords: backward method
author: Yu. M. Volin
author: G. M. Ostrovskij
reviewed by: M. Zuhair Nashed
MaRDI profile type: Publication
full work available at URL: 0898-1221(85)90188-9
OpenAlex ID: W1978670539
cites work: A simple automatic derivative evaluation program
cites work: Automatic Differentiation of Computer Programs
cites work: Automatic differentiation: techniques and applications
cites work: Q5636222
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 3958551