We study the convergence behavior of collocation schemes applied to approximate solutions of BVPs in linear index 1 DAEs which exhibit a critical point at the left boundary. Such a critical point of the DAE causes a singularity within the inherent ODE system. We focus our attention on the case when the inherent ODE system is singular with a singularity of the first kind, apply polynomial colloc...

This work introduces the weighted radial basis collocation method for boundary value problems. We first show that the employment of least-squares functional with quadrature rules constitutes an approximation of the direct collocation method. Standard radial basis collocation method, however, yields a larger solution error near boundaries. The residuals in the least-squares functional associated...

Collocations in the sense of idiosyncratic binary lexical co-occurrences are one of the biggest challenges for any language learner. Even advanced learners make collocation mistakes in that they literally translate collocation elements from their native tongue, create new words as collocation elements, choose a wrong subcategorization for one of the elements, etc. Therefore, automatic collocati...

We rigorously study a novel type of trigonometric Fourier collocation methods for solving multi-frequency oscillatory second-order ordinary differential equations (ODEs) q′′(t) + Mq(t) = f(q(t)) with a principal frequency matrix M ∈ Rd×d. If M is symmetric and positive semi-definite and f(q) = −∇U(q) for a smooth function U(q), then this is a multi-frequency oscillatory Hamiltonian system with ...

A collocation-Galerkin method is defined for Poisson's equation on the unit 2 square, using tensor products of continuous piecewise polynomials. Optimal L and Hq orders of convergence are established. This procedure requires fewer quadratures than the corresponding Galerkin procedure. Introduction. The collocation-Galerkin method was first introduced by Diaz [2], [3] for the two-point boundary ...

Abstract This paper describes an experiment that attempts to compare a range of existing collocation extraction techniques as well as the implementation of a new technique based on tests for lexical substitutability. After a description of the experiment details, the techniques are discussed with particular emphasis on any adaptations that are required in order to evaluate it in the way propose...

The immense explosion of geographically referenced data calls for efficient discovery of spatial knowledge. Spatial association analysis is a typical data mining approach for discovering spatial knowledge. Associate rules are patterns of form X→Y, where pattern Y is likely to occur when pattern X occurs. One of the most famous patterns, Diapers → Beer, is a typical association rule example. Spa...

There has been an increased interest in data generation approaches to grammatical error correction (GEC) using pseudo data. However, these suffer from several issues that make them inconvenient for real-world deployment including a demand large amounts of training On the other hand, some errors based on rules may not necessarily require amount if GEC models can realize generalization. This stud...

This report evaluates the impact of using a novel collocation segmentation method for phrase extraction in the standard phrase-based statistical machine translation approach. The collocation segmentation technique is implemented simultaneously in the source and target side. The resulting collocation segmentation is used to extract translation units. Experiments are reported in the Spanish-toEng...