In this paper, a well-conditioned collocation method is constructed for solving general p-th order linear differential equations with various types of boundary conditions. Based on a suitable Birkhoff interpolation, we obtain a new set of polynomial basis functions that results in a collocation scheme with two important features: the condition number of the linear system is independent of the n...

We propose a discrete collocation method for the boundary integral equations which arise from solving Laplace's equation u = 0. The Laplace's equation is deened on connected regions D in R 3 with a smooth boundary S. The piecewise polynomial interpolation in the parametrization variables along with the collocation method is used, and a numerical integration scheme for collocation integrals is g...

This article investigates the stability of the collocation method for the Radiosity equation. We introduce graded meshes and trial spaces of piecewise poynomials and prove stability for some modified collocation method. Next we show that graded meshes are necessary, even for linear convergence. The generation of triangulations which allow higher order approximations leads to geometrical problem...

Collocation and colligation are two closely related concepts associated with the distributional properties of linguistic items in actual language use. Specifically, collocation and colligation refer to the likelihood of co-occurrence of (two or more) lexical items and grammatical categories, respectively. Both terms have been attributed to J. R. Firth (1957: 194–195; 1968: 181–183; see Östman a...

‎in this paper‎, ‎an approach based on statistical spline model (ssm) and collocation method is proposed to solve volterra-fredholm integral equations‎. ‎the set of collocation nodes is chosen so that the points yield minimal error in the nodal polynomials‎. ‎under some standard assumptions‎, ‎we establish the convergence property of this approach‎. ‎numerical results on some problems are given...

Dissertation Abstract comprise words for which neither word can be substituted by a synonym or hyponym. Potential colloca-tions comprising certain adjacent part-of-speech tags are extracted from text. An online thesaurus and a lexical database of word classes are queried for synonyms and hypo nyms, respectively, for each potential collocation. These queries create potential challenger pairs, su...

A bstract This paper deserihes the treatment of lexical gaps, collocation information and idioms in the English to Portuguese machine translation system PORTUGA. The perspective is strictly bilingual, in the sense that all problems referenced above are considered to behmg to the tranM'cr phase, and not, as in other systems, to analysis or generation. The solution presented invokes a parser fi}r...