Superlinear Convergence of Krylov Subspace Methods for Self-Adjoint Problems in Hilbert Space
From MaRDI portal
Publication:5253775
DOI10.1137/140973050zbMath1312.65044OpenAlexW1480857162MaRDI QIDQ5253775
Ekkehard W. Sachs, Roland Griesse
Publication date: 28 May 2015
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/140973050
Hilbert spacesconjugate gradient methodKrylov subspace methodssuperlinear convergenceminimum residual method
Iterative numerical methods for linear systems (65F10) Existence theories for optimal control problems involving partial differential equations (49J20) Preconditioners for iterative methods (65F08)
Related Items
Learning physics-based models from data: perspectives from inverse problems and model reduction, Convergence of the conjugate gradient method with unbounded operators, Robust Superlinear Krylov Convergence for Complex Noncoercive Compact-Equivalent Operator Preconditioners, Analysis of the Barzilai-Borwein step-sizes for problems in Hilbert spaces, Krylov solvability under perturbations of abstract inverse linear problems, A Block Lanczos Method for Large-Scale Quadratic Minimization Problems with Orthogonality Constraints, A Convergence Analysis of the MINRES Method for Some Hermitian Indefinite Systems, A Data Scalable Augmented Lagrangian KKT Preconditioner for Large-Scale Inverse Problems, Krylov solvability of unbounded inverse linear problems, Krylov improvements of the Uzawa method for Stokes type operator matrices, PDE-Constrained Optimization with Local Control and Boundary Observations: Robust Preconditioners, Laplacian Preconditioning of Elliptic PDEs: Localization of the Eigenvalues of the Discretized Operator, On Krylov solutions to infinite-dimensional inverse linear problems, Parametrix for the inverse source problem of thermoacoustic tomography with reduced data, Analysis of Iterative Methods in Photoacoustic Tomography with Variable Sound Speed, Some Properties of the Arnoldi-Based Methods for Linear Ill-Posed Problems
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Composite convergence bounds based on Chebyshev polynomials and finite precision conjugate gradient computations
- Finite element approximation of the Navier-Stokes equations
- Equivalent operator preconditioning for elliptic problems
- A stopping criterion for the conjugate gradient algorithm in a finite element method framework
- The convergence rate of the minimal residual method for the Stokes problem
- Stability estimates and structural spectral properties of saddle point problems
- Operator preconditioning
- Superlinearly convergent PCG algorithms for some nonsymmetric elliptic systems
- Error estimation in preconditioned conjugate gradients
- A note on preconditioners and scalar products in Krylov subspace methods for self-adjoint problems in Hilbert space
- Preconditioning discretizations of systems of partial differential equations
- Some Convergence Properties of the Conjugate Gradient Method in Hilbert Space
- Preconditioned Conjugate Gradient Method for Optimal Control Problems with Control and State Constraints
- ON THE RATE OF CONVERGENCE OF THE CONJUGATE GRADIENT METHOD FOR LINEAR OPERATORS IN HILBERT SPACE
- Mesh Independent Superlinear PCG Rates Via Compact-Equivalent Operators
- From Functional Analysis to Iterative Methods
- Some History of the Conjugate Gradient and Lanczos Algorithms: 1948–1976
- Some Superlinear Convergence Results for the Conjugate Gradient Method
- A Preconditioned Iterative Method for Saddlepoint Problems
- Solution of Sparse Indefinite Systems of Linear Equations
- A Lanczos Method for a Class of Nonsymmetric Systems of Linear Equations
- Iterative Krylov Methods for Large Linear Systems
- Quantum Theory for Mathematicians
- Iterative Solution of Nonlinear Equations in Several Variables
- Preconditioning and convergence in the right norm
- Convergence Analysis of Krylov Subspace Iterations with Methods from Potential Theory
- The Conjugate Gradient Method for Linear and Nonlinear Operator Equations
- Methods of conjugate gradients for solving linear systems
- Functional analysis