Singularity Analysis Via the Iterated Kernel Method

Singularity Analysis Via the Iterated Kernel Method

We provide exact and asymptotic counting formulas for five singular lattice path models in the quarter plane. Furthermore, we prove that these models have a non D-finite generating function. Résumé Nous présentons des résultats énumératives pour les cinq modèles de marches dans le quart de plan dites “singulière”. Nous prouvons que ces modéles sont non-holonome.

Superconvergence of the Iterated Degenerate Kernel Method

Singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel

In a recent paper [3], Y. Cao and Y. Xu established the Galerkin method for weakly singular Fredholm integral equations that preserves the singularity of the solution. Their Galerkin method provides a numerical solution that is a linear combination of a certain class of basis functions which includes elements that reflect the singularity of the solution. The purpose of this paper is to extend t...

Iterated Transformation-Kernel Density Estimation

Transformation from a parametric family can improve the performance of kernel density estimation. In this paper, we give two data-driven estimators for the optimal transformation parameter. We demonstrate that multiple families of transformations can be employed at the same time, and there can be beneets to iterating this process. The transformation scheme can be expected to rst pick the right ...

The Iterated Projection Method for Integro-differential Equations with Cauchy Kernel

In this paper we propose the iterated projection method for the approximate solution of an integro-differential equations with Cauchy kernel in L2([−1, 1],C) using Legendre polynomials. We prove the convergence of the method. A system of linear equations is to be solved. Numerical examples illustrate the theoretical results. AMS Mathematics Subject Classification : 45E05, 35J15.