Multilevel methods for the approximation of singular solutions of completely continuous operator equations
type: Item
instance of: scholarly article
title: Multilevel methods for the approximation of singular solutions of completely continuous operator equations
zbMATH Open document ID: 0776.65041
author: Igor Moret
published in: Journal of Integral Equations and Applications
publication date: 1993-12-01T00:00:00Z
review text: Multilevel methods in Banach spaces are considered for approximating singular solutions of the parameter-dependent problem \(u-K(u,\lambda)=0\), where \(K: (u,\lambda)\in U\times\mathbb{R}^ p\to U\) is a completely continuous \(C^ \nu\)-mapping \((\nu\geq 1)\) and \(U\) is a Banach space. By embedding the singular problem into an extended system, the author discusses an iterative method to approximate the solution with incorporation of multilevel methods for the linearized problems in Banach spaces. Convergence of the method is established under appropriate approximations of \(K\) with collectively compact operators and projections.
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 205198
zbMATH Keywords: completely continuous operator equations
zbMATH Keywords: multilevel methods
zbMATH Keywords: convergence
zbMATH Keywords: Banach spaces
zbMATH Keywords: singular solutions
zbMATH Keywords: iterative method
zbMATH Keywords: collectively compact operators
reviewed by: Zhen Mei
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/jiea/1181075731
OpenAlex ID: W2039044775
cites work: Q5635885
cites work: Q4124250
cites work: The Numerical Solution of a Bifurcation Problem
cites work: Projection and Iterated Projection Methods for Nonlinear Integral equations
cites work: The discrete Galerkin method for nonlinear integral equations
cites work: Über die numerische Behandlung von Integralgleichungen nach der Quadraturformelmethode
cites work: An automatic procedure for the calculation of bifurcation points of integral equations
cites work: Q3309016
cites work: On Solving Nonlinear Equations with Simple Singularities or Nearly Singular Solutions
cites work: Characterization and Computation of Generalized Turning Points
cites work: The approximation of generalized turning points by projection methods with superconvergence to the critical parameter
cites work: Q3727300
cites work: Multiple Grid Methods for the Solution of Fredholm Integral Equations of the Second Kind
cites work: Q3474846
cites work: Superconvergence of a Collocation-Type Method for Simple Turning Points of Hammerstein Equations
cites work: A New Collocation-Type Method for Hammerstein Integral Equations
cites work: Differentiability and convergence for compact nonlinear operators
cites work: Computing simple bifurcation points using a minimally extended system of nonlinear equations
cites work: Improvement by Iteration for Compact Operator Equations
cites work: Q3900934
DOI: 10.1216/JIEA/1181075731
description: scientific article; zbMATH DE number 205198