Superconvergent Nyström and degenerate kernel methods for eigenvalue problems
type: Item
instance of: scholarly article
title: Superconvergent Nyström and degenerate kernel methods for eigenvalue problems
zbMATH Open document ID: 1228.65241
author: C. Alouch
author: D. Sbibih
author: M. Tahrichi
author: P. Sablonnière
published in: Applied Mathematics and Computation
publication date: 2011-06-28T00:00:00Z
review text: The authors propose new superconvergent Nyström and degenerate kernel methods based on projections onto the space of discontinuous piecewise polynomials of degree \(\leq R - 1\) for the approximate solution of eigenvalue problems for compact integral operators. Similar to a method studied by \textit{R. P. Kulkarni}, [Math. Comput. 75, No.~254, 847--857 (2006; Zbl 1090.65151)], convergence orders 4r for the eigenvalue approximation and 3r for spectral subspace approximation are obtained for sufficiently smooth kernels, but the proposed methods are simpler and faster to implement. The authors consider also application of the methods to the case of discontinuous integral kernels along the diagonal and prove superconvergence results. Numerical examples confirm the theoretical results.
reviewed by: Gunther Schmidt
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45C05
zbMATH DE Number: 5914099
zbMATH Keywords: eigenvalue problems
zbMATH Keywords: linear integral operator
zbMATH Keywords: Nyström method
zbMATH Keywords: degenerate kernel method
zbMATH Keywords: discontinuous splines
zbMATH Keywords: eigenvector
zbMATH Keywords: superconvergence
zbMATH Keywords: compact integral operators
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: j.amc.2011.01.098
OpenAlex ID: W2005498811
cites work: Spectral computations for bounded operators
cites work: Collocation at Gaussian Points
cites work: A method for obtaining bounds on eigenvalues and eigenfunctions by solving non-homogeneous integral equations
cites work: Spectral Approximation for Compact Operators
cites work: Q3666156
cites work: The iterated projection solution for the Fredholm integral equation of second kind
cites work: A New Superconvergent Projection Method for Approximate Solutions of Eigenvalue Problems
cites work: On improvement of the iterated Galerkin solution of the second kind integral equations
cites work: A degenerate kernel method for eigenvalue problems of compact integral operators
cites work: The projection Kantorovich method for eigenvalue problems
cites work: Integral equations with diagonal and boundary singularities of the kernel
cites work: Spectral approximation for compact integral operators by degenerate kernel methods
DOI: 10.1016/J.AMC.2011.01.098
description: scientific article; zbMATH DE number 5914099