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Automatic differentiation and its program realization

Jan Hartman, Ladislav Lukšan, Jan Zítko (2009)

Kybernetika

Automatic differentiation is an effective method for evaluating derivatives of function, which is defined by a formula or a program. Program for evaluating of value of function is by automatic differentiation modified to program, which also evaluates values of derivatives. Computed values are exact up to computer precision and their evaluation is very quick. In this article, we describe a program realization of automatic differentiation. This implementation is prepared in the system UFO, but its...

Automatic differentiation platform : design

Christèle Faure (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Automatic differentiation (AD) has proven its interest in many fields of applied mathematics, but it is still not widely used. Furthermore, existing numerical methods have been developed under the hypotheses that computing program derivatives is not affordable for real size problems. Exact derivatives have therefore been avoided, or replaced by approximations computed by divided differences. The hypotheses is no longer true due to the maturity of AD added to the quick evolution of machine capacity....

Automatic Differentiation Platform: Design

Christèle Faure (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Automatic differentiation (AD) has proven its interest in many fields of applied mathematics, but it is still not widely used. Furthermore, existing numerical methods have been developed under the hypotheses that computing program derivatives is not affordable for real size problems. Exact derivatives have therefore been avoided, or replaced by approximations computed by divided differences. The hypotheses is no longer true due to the maturity of AD added to the quick evolution of machine capacity....

Automatic Identification of False Friends in Parallel Corpora: Statistical and Semantic Approach

Nakov, Svetlin (2009)

Serdica Journal of Computing

False friends are pairs of words in two languages that are perceived as similar but have different meanings. We present an improved algorithm for acquiring false friends from sentence-level aligned parallel corpus based on statistical observations of words occurrences and co-occurrences in the parallel sentences. The results are compared with an entirely semantic measure for cross-lingual similarity between words based on using the Web as a corpus through analyzing the words’ local contexts extracted...

Automaticity IV : sequences, sets, and diversity

Jeffrey Shallit (1996)

Journal de théorie des nombres de Bordeaux

This paper studies the descriptional complexity of (i) sequences over a finite alphabet ; and (ii) subsets of N (the natural numbers). If ( s ( i ) ) i 0 is a sequence over a finite alphabet Δ , then we define the k -automaticity of s , A s k ( n ) , to be the smallest possible number of states in any deterministic finite automaton that, for all i with 0 i n , takes i expressed in base k as input and computes s ( i ) . We give examples of sequences that have high automaticity in all bases k ; for example, we show that the characteristic...

Autour de nouvelles notions pour l’analyse des algorithmes d’approximation : formalisme unifié et classes d’approximation

Marc Demange, Vangelis Paschos (2002)

RAIRO - Operations Research - Recherche Opérationnelle

The main objective of the polynomial approximation is the development of polynomial time algorithms for NP-hard problems, these algorithms guaranteeing feasible solutions lying “as near as possible” to the optimal ones. This work is the fist part of a couple of papers where we introduce the key-concepts of the polynomial approximation and present the main lines of a new formalism. Our purposes are, on the one hand, to present this theory and its objectives and, on the other hand, to discuss the...

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