In this article, we propose the use of partitioning and clustering methods as an alternative to Gaussian quadrature for stochastic collocation (SC). The key idea is to use cluster centers as the nodes for collocation. In this way, we can extend the use of collocation methods to uncertainty propagation with multivariate, correlated input. The approach is particularly useful in situations where t...

The selection of features is critical in providing discriminative information for classifiers in Word Sense Disambiguation (WSD). Uninformative features will degrade the performance of classifiers. Based on the strong evidence that an ambiguous word expresses a unique sense in a given collocation, this paper reports our experiments on automatic WSD using collocation as local features based on t...

A long-standing open question associated with the use of collocation methods for boundary value ordinary differential equations is concerned with the development of a high order continuous solution approximation to augment the high order discrete solution approximation, obtained at the mesh points which subdivide the problem interval. It is well known that the use of collocation at Gauss points...

Quartic-Spline Collocation Methods for Fourth-Order Two-Point Boundary Value Problems Ying Zhu Master of Science Graduate Department of Computer Science University of Toronto 2001 This thesis presents numerical methods for the solution of general linear fourth-order boundary value problems in one dimension. The methods are based on quartic splines, that is, piecewise quartic polynomials with C3...

Collocations play a significant role in second language acquisition. In order to be able to offer efficient support to learners, an NLP-based CALL environment for learning collocations should be based on a representative collocation error annotated learner corpus. However, so far, no theoretically-motivated collocation error tag set is available. Existing learner corpora tag collocation errors ...

In this paper, consideration is given to how aliasing errors, introduced when evaluating nonlinear products, inexactly affect the solution of Galerkin spectral/hp element polynomial discretisations on triangles. A theoretical discussion is presented of how aliasing errors are introduced by a collocation projection onto a set of quadrature points insufficient for exact integration, and consider ...

This study investigates the influence of using five web-based practice units on English verb-noun collocations with the design of a web-based Chinese-English bilingual concordancer (keyword retrieval program) on collocation learning. Thirty-two college EFL students participated by taking a pre-test and two post-tests, and responding to a background questionnaire and an evaluation questionnaire....

A new moving mesh method is introduced for solving time dependent partial diierential equations (PDEs) in divergence form. The method uses a cell-averaging cubic Hermite collocation discretization for the physical PDEs and a three point nite diierence discretization for the PDE which determines the moving mesh. Numerical results are presented for a selection of diicult benchmark problems, inclu...

In this paper, a Chebyshev spectral collocation domain decomposition (DD) semidiscretization by using a grid mapping, derived by Kosloff and Tal-Ezer in space is applied to the numerical solution of the generalized Burger’s–Huxley (GBH) equation. To reduce roundoff error in computing derivatives we use the above mentioned grid mapping. In this work, we compose the Chebyshev spectral collocation...