On the fast and fully discretized solution of integral and pseudo-differential equations on smooth curves
type: Item
instance of: scholarly article
title: On the fast and fully discretized solution of integral and pseudo-differential equations on smooth curves
zbMATH Open document ID: 1008.65098
DOI: 10.1007/PL00011226
author: Robert Plato
author: G. Vainikko
published in: Calcolo
publication date: 2002-12-17T00:00:00Z
review text: The paper is devoted to the numerical solution of pseudo-differential equations on smooth closed curves by a fully discrete version of the trigonometric Galerkin method. For the discrete Galerkin equations, approximate solutions with small residuals are considered, and optimal error estimates in periodic Sobolev norms are obtained. Using the conjugate gradient method of Hestenes and Stiefel applied to the normal equations, the authors provide an iteration scheme where the approximations can be obtained by a total number of \(O(N\log N)\) arithmetical operations. The influence of noise in the model of the problem as well as in the right-hand side is examined, and some numerical examples are presented.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 65T40
Mathematics Subject Classification ID: 65N38
zbMATH DE Number: 1846808
zbMATH Keywords: periodic pseudodifferential equations
zbMATH Keywords: trigonometric Galerkin method
zbMATH Keywords: CGNR method
zbMATH Keywords: fast solver
reviewed by: Johannes Elschner
MaRDI profile type: Publication
full work available at URL: pl00011226
OpenAlex ID: W2086429936
description: scientific article; zbMATH DE number 1846808