Récursivité

Résumé

La récursivité est une démarche qui fait référence à l'objet même de la démarche à un moment du processus. En d'autres termes, c'est une démarche dont la description mène à la répétition d'une même règle. Ainsi, les cas suivants constituent des cas concrets de récursivité :

décrire un processus dépendant de données en faisant appel à ce même processus sur d'autres données plus « simples » ;
montrer une image contenant des images similaires ;
définir un concept en invoquant ce même concept ;
écrire un algorithme qui s'invoque lui-même ;
définir une structure à partir de l'une au moins de ses sous-structures ;
faire pointer un article de Wikipédia vers lui-même ou vers un article qui, par une succession de pointeurs, pointe vers l'article dont on est parti ; ainsi dans l'article que vous lisez, l'expression « pétition de principe » pointe vers un article qui pointe vers le présent article.

En informatique Algorithme récursif vignette|Un arbre binaire est une struc

Source officielle

https://fr.wikipedia.org/wiki/R%C3%A9cursivit%C3%A9

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Cours associés (24)

Discrete mathematics is a discipline with applications to almost all areas of study. It provides a set of indispensable tools to computer science in particular. This course reviews (familiar) topics as diverse as mathematical reasoning, combinatorics, discrete structures & algorithmic thinking.

We introduce formal verification as an approach for developing highly reliable systems. Formal verification finds proofs that computer systems work under all relevant scenarios. We will learn how to use formal verification tools and explain the theory and the practice behind them.

Students learn several implementation techniques for modern functional and object-oriented programming languages. They put some of them into practice by developing key parts of a compiler and run time system for a simple functional programming language.

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Séances de cours associées (69)

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Planner9, a HTN planner distributed on groups of miniature mobile robots

Stéphane Magnenat, Francesco Mondada, Martin Voelkle

Autonomous mobile robots are promising tools for operations in environments that are difficult to access for humans. When these environments are dynamic and non-deterministic, like in collapsed buildings, the robots must coordinate their actions and the use of resources using planning. This paper presents Planner9, a hierarchical task network (HTN) planner that runs on groups of miniature mobile robots. These robots have limited computational power and memory, but are well connected through Wi-Fi. Planner9 takes advantage of this connectivity to distribute the planning over different robots. We have adapted the HTN algorithm to perform parallel search using A* and to limit the number of search nodes through lifting. We show that Planner9 scales well with the number of robots, even on non-linear tasks that involve recursions in their decompositions. We show that contrary to JSHOP2, Planner9 finds optimal plans.

Springer2009

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MATHICSE Technical Report : Regularity and sparse approximation of the recursive first moment equations for the lognormal Darcy problem

Francesca Bonizzoni, Fabio Nobile

We study the Darcy boundary value problem with log-normal permeability field. We adopt a perturbation approach, expanding the solution in Taylor series around the nominal value of the coefficient, and approximating the expected value of the stochastic solution of the PDE by the expected value of its Taylor polynomial. The recursive deterministic equation satisfied by the expected value of the Taylor polynomial (first moment equation) is formally derived. Well-posedness and regularity results for the recursion are proved to hold in Sobolev space-valued Hölder spaces with mixed regularity. The recursive first moment equation is then discretized by means of a sparse approximation technique, and the convergence rates are derived.

MATHICSE2020

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Regularity and sparse approximation of the recursive first moment equations for the lognormal Darcy problem

Francesca Bonizzoni, Fabio Nobile

We study the Darcy boundary value problem with lognormal permeability field. We adopt a perturbation approach, expanding the solution in Taylor series around the nominal value of the coefficient, and approximating the expected value of the stochastic solution of the PDE by the expected value of its Taylor polynomial. The recursive deterministic equation satisfied by the expected value of the Taylor polynomial (first moment equation) is formally derived. Well-posedness and regularity results for the recursion are proved to hold in Sobolev space-valued Hölder spaces with mixed regularity. The recursive first moment equation is then discretized by means of a sparse approximation technique, and the convergence rates are derived.

2020

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