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Collocation

About: Collocation is a research topic. Over the lifetime, 5108 publications have been published within this topic receiving 88028 citations.


Papers
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Journal ArticleDOI
TL;DR: The emergence of a new view of language and the computer technology associated with it is charted in this study.
Abstract: Designed for English language teachers and other educators, this study charts the emergence of a new view of language and the computer technology associated with it.

3,113 citations

Journal ArticleDOI
TL;DR: A high-order stochastic collocation approach is proposed, which takes advantage of an assumption of smoothness of the solution in random space to achieve fast convergence and requires only repetitive runs of an existing deterministic solver, similar to Monte Carlo methods.
Abstract: Recently there has been a growing interest in designing efficient methods for the solution of ordinary/partial differential equations with random inputs. To this end, stochastic Galerkin methods appear to be superior to other nonsampling methods and, in many cases, to several sampling methods. However, when the governing equations take complicated forms, numerical implementations of stochastic Galerkin methods can become nontrivial and care is needed to design robust and efficient solvers for the resulting equations. On the other hand, the traditional sampling methods, e.g., Monte Carlo methods, are straightforward to implement, but they do not offer convergence as fast as stochastic Galerkin methods. In this paper, a high-order stochastic collocation approach is proposed. Similar to stochastic Galerkin methods, the collocation methods take advantage of an assumption of smoothness of the solution in random space to achieve fast convergence. However, the numerical implementation of stochastic collocation is trivial, as it requires only repetitive runs of an existing deterministic solver, similar to Monte Carlo methods. The computational cost of the collocation methods depends on the choice of the collocation points, and we present several feasible constructions. One particular choice, based on sparse grids, depends weakly on the dimensionality of the random space and is more suitable for highly accurate computations of practical applications with large dimensional random inputs. Numerical examples are presented to demonstrate the accuracy and efficiency of the stochastic collocation methods.

1,637 citations

Journal ArticleDOI
TL;DR: In this article, an algorithm for the direct numerical solution of an optimal control problem is given, which employs cubic polynomials to represent state variables, linearly interpolates control variables, and uses collocation to satisfy the differential equations.
Abstract: An algorithm for the direct numerical solution of an optimal control problem is given. The method employs cubic polynomials to represent state variables, linearly interpolates control variables, and uses collocation to satisfy the differential equations. This representation transforms the optimal control problem to a mathematical programming problem which is solved by sequential quadratic programming. The method is easy to program for a very general trajectory optimization problem and is shown to be very efficient for several sample problems. Results are compared with solutions obtained with other methods.

1,100 citations

Book
01 Jan 1975
TL;DR: In this article, Lagrangians interpolates Hermitian interpolates polynomial splines and generalizations approximating functions of several variables fundamentals for variational methods the finite element method the method of collocation.
Abstract: Introductory ideas Lagrangian interpolates Hermitian interpolates polynomial splines and generalizations approximating functions of several variables fundamentals for variational methods the finite element method the method of collocation.

1,014 citations

Journal Article
Frank Smadja1
TL;DR: A set of techniques based on statistical methods for retrieving and identifying collocations from large textual corpora, based on some original filtering methods that allow the production of richer and higher-precision output are described.
Abstract: Natural languages are full of collocations, recurrent combinations of words that co-occur more often than expected by chance and that correspond to arbitrary word usages. Recent work in lexicography indicates that collocations are pervasive in English; apparently, they are common in all types of writing, including both technical and nontechnical genres. Several approaches have been proposed to retrieve various types of collocations from the analysis of large samples of textual data. These techniques automatically produce large numbers of collocations along with statistical figures intended to reflect the relevance of the associations. However, none of these techniques provides functional information along with the collocation. Also, the results produced often contained improper word associations reflecting some spurious aspect of the training corpus that did not stand for true collocations.In this paper, we describe a set of techniques based on statistical methods for retrieving and identifying collocations from large textual corpora. These techniques produce a wide range of collocations and are based on some original filtering methods that allow the production of richer and higher-precision output. These techniques have been implemented and resulted in a lexicographic tool, Xtract. The techniques are described and some results are presented on a 10 million-word corpus of stock market news reports. A lexicographic evaluation of Xtract as a collocation retrieval tool has been made, and the estimated precision of Xtract is 80%.

923 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20226
2021325
2020290
2019304
2018328
2017261