The method of alternating projections and the method of subspace corrections in Hilbert space

DOI10.1090/S0894-0347-02-00398-3zbMath0999.47015OpenAlexW1530115438MaRDI QIDQ4330566

Publication date: 13 May 2002

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0894-0347-02-00398-3

zbMATH Keywords

domain decomposition multigrid method of subspace corrections Babuška-Brezzi conditions linear variational problem method of alternate projections product of nonexpansive operators

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) General theory of numerical analysis in abstract spaces (65J05) Iterative numerical methods for linear systems (65F10) Linear operator approximation theory (47A58) Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10) Numerical methods of relaxation type (49M20) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Applications of operator theory in numerical analysis (47N40)

Related Items (only showing first 100 items - show all)

An error-resilient redundant subspace correction method ⋮ Additive Schwarz methods for convex optimization with backtracking ⋮ The rate of convergence in the method of alternating projections ⋮ Multilevel preconditioners for reaction-diffusion problems with discontinuous coefficients ⋮ Meta-mgnet: meta multigrid networks for solving parameterized partial differential equations ⋮ Arbitrarily Slow Convergence of Sequences of Linear Operators: A Survey ⋮ A robust preconditioner for higher order finite element discretizations in linear elasticity ⋮ Uniform subspace correction preconditioners for discontinuous Galerkin methods with \(hp\)-refinement ⋮ Analysis of multilevel methods for eddy current problems ⋮ Convergence Properties of the Randomized Extended Gauss--Seidel and Kaczmarz Methods ⋮ A generalization of the Friedrichs angle and the method of alternating projections ⋮ Solving systems of phaseless equations via Kaczmarz methods: a proof of concept study ⋮ The rate of convergence for the cyclic projections algorithm. I: Angles between convex sets ⋮ A New Analytical Framework for the Convergence of Inexact Two-Grid Methods ⋮ Alternating Least Squares as Moving Subspace Correction ⋮ Uniform convergence of multigrid V-cycle on adaptively refined finite element meshes for second order elliptic problems ⋮ On greedy randomized block Kaczmarz method for consistent linear systems ⋮ Randomized Kaczmarz with averaging ⋮ A survey on numerical methods for spectral space-fractional diffusion problems ⋮ A geometric data structure for parallel finite elements and the application to multigrid methods with block smoothing ⋮ Improved convergence bounds for two-level methods with an aggressive coarsening and massive polynomial smoothing ⋮ Nearly optimal convergence result for multigrid with aggressive coarsening and polynomial smoothing. ⋮ Slow convergence of sequences of linear operators. II: Arbitrarily slow convergence ⋮ High-order extended finite element methods for solving interface problems ⋮ Alternating projections on nontangential manifolds ⋮ Optimal scaling parameters for sparse grid discretizations ⋮ Optimal multilevel adaptive FEM for the Argyris element ⋮ Block Kaczmarz method with inequalities ⋮ Uniformly convergent iterative methods for discontinuous Galerkin discretizations ⋮ Algebraic multigrid methods ⋮ A two‐grid SA‐AMG convergence bound that improves when increasing the polynomial degree ⋮ An additive analysis of multiplicative Schwarz methods ⋮ Multiplicative Schwarz Methods for Discontinuous Galerkin Approximations of Elliptic Problems ⋮ Additive Schwarz Methods for Convex Optimization as Gradient Methods ⋮ A randomized approximation algorithm for the minimal-norm static-output-feedback problem ⋮ Multilevel approximation of Gaussian random fields: Fast simulation ⋮ An Additive Schwarz Analysis for Multiplicative Schwarz Methods: General Case ⋮ A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations ⋮ Multigrid methods for a quad-curl problem based on \(C^0\) interior penalty method ⋮ Two-level additive Schwarz methods for discontinuous Galerkin approximations of the biharmonic equation ⋮ UNIFORM CONVERGENT MULTIGRID METHODS FOR ELLIPTIC PROBLEMS WITH STRONGLY DISCONTINUOUS COEFFICIENTS ⋮ Paved with good intentions: analysis of a randomized block Kaczmarz method ⋮ Greedy and randomized versions of the multiplicative Schwarz method ⋮ Additive regression with Hilbertian responses ⋮ Efficient Low-Order Refined Preconditioners for High-Order Matrix-Free Continuous and Discontinuous Galerkin Methods ⋮ Multigrid methods for saddle point problems: Stokes and Lamé systems ⋮ Unnamed Item ⋮ Optimal multilevel methods for graded bisection grids ⋮ Accelerating the alternating projection algorithm for the case of affine subspaces using supporting hyperplanes ⋮ Randomized block Kaczmarz method with projection for solving least squares ⋮ A review of numerical methods for nonlinear partial differential equations ⋮ Hierarchical Argyris finite element method for adaptive and multigrid algorithms ⋮ Uniform convergence of V-cycle multigrid algorithms for two-dimensional fractional Feynman-Kac equation ⋮ A geometric-based algebraic multigrid method for higher-order finite element equations in two-dimensional linear elasticity ⋮ Optimality of local multilevel methods on adaptively refined meshes for elliptic boundary value problems ⋮ A uniform additive Schwarz preconditioner for high-order discontinuous Galerkin approximations of elliptic problems ⋮ Alternating projection method for sparse model updating problems ⋮ An algebraic multilevel method for anisotropic elliptic equations based on subgraph matching ⋮ An improved convergence analysis of smoothed aggregation algebraic multigrid ⋮ Multigrid methods for saddle point systems using constrained smoothers ⋮ Comparison of bounds for V-cycle multigrid ⋮ Preconditioning a class of fourth order problems by operator splitting ⋮ Regularity and multigrid analysis for Laplace-type axisymmetric equations ⋮ Alternating oblique projections for coupled linear systems ⋮ Schwarz domain decomposition preconditioners for discontinuous Galerkin approximations of elliptic problems: non-overlapping case ⋮ Schwarz methods for quasi stationary distributions of Markov chains ⋮ An algebraic multigrid method for finite element systems on criss-cross grids ⋮ BPX preconditioners for isogeometric analysis using (truncated) hierarchical B-splines ⋮ Uniform convergence of V-cycle multigrid finite element method for one-dimensional time-dependent fractional problem ⋮ On an energy minimizing basis for algebraic multigrid methods ⋮ Angles between infinite dimensional subspaces with applications to the Rayleigh-Ritz and alternating projectors methods ⋮ A posteriori error estimates of finite element methods by preconditioning ⋮ Positive Approximations of the Inverse of Fractional Powers of SPD M-Matrices ⋮ A nearly optimal multigrid method for general unstructured grids ⋮ Spectral multiscale finite element for nonlinear flows in highly heterogeneous media: a reduced basis approach ⋮ Uniform convergence of multigrid methods for adaptive meshes ⋮ The rate of convergence for the cyclic projections algorithm. III: Regularity of convex sets ⋮ Decomposition into subspaces preconditioning: abstract framework ⋮ An optimal multigrid algorithm for the combining \(P_1\)-\(Q_1\) finite element approximations of interface problems based on local anisotropic fitting meshes ⋮ BPX Preconditioner for Nonstandard Finite Element Methods for Diffusion Problems ⋮ On the method of reflections ⋮ Parallel subspace correction methods for nearly singular systems ⋮ Optimal Finite Element Methods for Interface Problems ⋮ High-order finite element methods for interface problems: theory and implementations ⋮ Smooth backfitting for errors-in-variables varying coefficient regression models ⋮ Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models ⋮ Uniform stability analysis of Austin, Manteuffel and McCormick finite elements and fast and robust iterative methods for the Stokes-like equations ⋮ Uniformly Stable Discontinuous Galerkin Discretization and Robust Iterative Solution Methods for the Brinkman Problem ⋮ When does two-grid optimality carry over to the V-cycle? ⋮ MgNet: a unified framework of multigrid and convolutional neural network ⋮ Randomized and fault-tolerant method of subspace corrections ⋮ Finite element approximation of multi-scale elliptic problems using patches of elements ⋮ A two-level algorithm for the weak Galerkin discretization of diffusion problems ⋮ Convergence analysis for Kaczmarz-type methods in a Hilbert space framework ⋮ A family of independent variable Eddington factor methods with efficient preconditioned iterative solvers ⋮ Locking-Free Enriched Galerkin Method for Linear Elasticity ⋮ Convergence Analysis of Inexact Two-Grid Methods: A Theoretical Framework ⋮ On robustly convergent and efficient iterative methods for anisotropic radiative transfer ⋮ Ritt operators and convergence in the method of alternating projections ⋮ Algebraic multilevel iteration method for lowest order Raviart-Thomas space and applications

Cites Work

This page was built for publication: The method of alternating projections and the method of subspace corrections in Hilbert space