this paper may be regarded as a new numerical method for the analysis of triangular thin plates using the natural area coordinates. previous studies on the solution of triangular plates with different boundary conditions are mostly based on the rayleigh-ritz principle which is performed in the cartesian coordinates. consequently, manipulation of the geometry and numerical calculation of the int...

FOM and GMRES are Krylov subspace iterative methods for solving nonsymmetric linear systems. The Ritz values are approximate eigenvalues, which can be computed cheaply within these algorithms. In this paper, we generalise the concept of Harmonic Ritz values, introduced by Paige et al. for symmetric matrices, to nonsymmetric matrices. We show that the zeroes of the residual polynomials of FOM an...

where the values of the constants Ai, A2 and Pi, P2 are not simultaneously zero. Several methods have been proposed to determine the proper elements (i.e. eigenvalues and eigenfunctions) of Sturm-Liouville equations. Most of them have been reviewed by Kopal [1], but we shall examine one of them, the so called Rayleigh-Ritz method, in order to explain the main defect they have in common and to j...

Syntactic configurations used in collocation extraction are highly divergent from one system to another, this questioning the validity of results and making comparative evaluation difficult. We describe a corpus-driven approach for inferring an exhaustive set of configurations from actual data by finding, with a parser, all the productive syntactic associations, then by appealing to human exper...

This paper presents a status quo of an ongoing research study of collocations – an essential linguistic phenomenon having a wide spectrum of applications in the field of natural language processing. The core of the work is an empirical evaluation of a comprehensive list of automatic collocation extraction methods using precision-recall measures and a proposal of a new approach integrating multi...

This paper reports on the development of a collocation extraction system that is designed within a commercial machine translation system in order to take advantage of the robust syntactic analysis that the system offers and to use this analysis to refine collocation extraction. Embedding the extraction system also addresses the need to provide information about the source language collocations ...

We develop spectral collocation methods for fractional differential equations with variable order with two end-point singularities. Specifically, we derive three-term recurrence relations for both integrals and derivatives of the weighted Jacobi polynomials of the form 1 x μ1 1 Æ x 2P a,b j x a, b, μ1, μ2 Æ1 , which leads to the desired differentiation matrices. We apply the new differentiation...

In this article, an implicit hybrid method of order six is developed for the direct solution of second order ordinary differential equations using collocation and interpolation approach. To derive this method, the approximate solution power series is interpolated at the first and off-step points and its second and third derivatives are collocated at all points in the given interval. Besides hav...

This paper presents an alternative approach for the computation of trajectory segments on slow manifolds of saddle type. This approach is based on iterative methods rather than collocation-type methods. Compared to collocation methods, which require mesh refinements to ensure uniform convergence with respect to , appropriate estimates are directly attainable using the method of this paper. The ...

The IDR method of Sonneveld and van Gijzen [SIAM J. Sci. Comput., 31:1035–1062, 2008] is shown to be a Petrov-Galerkin (projection) method with a particular choice of left Krylov subspaces; these left subspaces are rational Krylov spaces. Consequently, other methods, such as BiCGStab and ML(s)BiCGStab, which are mathematically equivalent to some versions of IDR, can also be interpreted as Petro...