A theoretical overview of Krylov subspace methods
From MaRDI portal
Publication:1917418
DOI10.1016/0168-9274(95)00084-4zbMath0854.65031OpenAlexW2035854297MaRDI QIDQ1917418
Publication date: 7 July 1996
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0168-9274(95)00084-4
Related Items
Lanczos-type variants of the COCR method for complex nonsymmetric linear systems, Special issue: Developments and trends in iterative methods for large systems of equations -- in memoriam Rüdiger Weiss. Minisymposium: 16th IMACS world congress, Lausanne, Switzerland, August 21--25, 2000, On global Hessenberg based methods for solving Sylvester matrix equations, Derivation of BiCG from the conditions defining Lanczos' method for solving a system of linear equations, Iterative solution of linear systems in the 20th century
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Preconditioning strategies for models of incompressible flow
- A breakdown-free Lanczos type algorithm for solving linear systems
- On conjugate gradient type methods and polynomial preconditioners for a class of complex non-Hermitian matrices
- On the rate of convergence of the preconditioned conjugate gradient method
- QMR: A quasi-minimal residual method for non-Hermitian linear systems
- Avoiding breakdown in the CGS algorithm
- Avoiding breakdown and near-breakdown in Lanczos type algorithms
- Stationary and almost stationary iterative (k,l)-step methods for linear and nonlinear systems of equations
- A historical overview of iterative methods
- Implementations of the GMRES method
- BiCGstab(\(l\)) and other hybrid Bi-CG methods
- BiCGstab(\(l\)) for linear equations involving unsymmetric matrices with complex spectrum
- Minimization properties and short recurrences for Krylov subspace methods
- Complex conjugate gradient methods
- A comparison of GMRES and CGSTAB accelerations for incompressible Navier- Stokes problems
- Reliable updated residuals in hybrid Bi-CG methods
- An engineering approach to generalized conjugate gradient methods and beyond
- Peaks, plateaus, numerical instabilities in a Galerkin minimal residual pair of methods for solving \(Ax=b\)
- Generalized conjugate gradient squared
- A Taxonomy for Conjugate Gradient Methods
- A Look-Ahead Lanczos Algorithm for Unsymmetric Matrices
- GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
- CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
- Some History of the Conjugate Gradient and Lanczos Algorithms: 1948–1976
- Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
- A Completed Theory of the Unsymmetric Lanczos Process and Related Algorithms, Part I
- Changing the Norm in Conjugate Gradient Type Algorithms
- Solution of Sparse Indefinite Systems of Linear Equations
- Variants of BICGSTAB for Matrices with Complex Spectrum
- A Breakdown-Free Variation of the Nonsymmetric Lanczos Algorithms
- Residual Smoothing Techniques for Iterative Methods
- Iterative Solution Methods
- Error-Minimizing Krylov Subspace Methods
- Composite Step Product Methods for Solving Nonsymmetric Linear Systems
- Orthogonal Error Methods
- An Implementation of the Look-Ahead Lanczos Algorithm for Non-Hermitian Matrices
- A Transpose-Free Quasi-Minimal Residual Algorithm for Non-Hermitian Linear Systems
- The method of minimum iterations with minimum errors for a system of linear algebraic equations with a symmetrical matrix
- Methods of conjugate gradients for solving linear systems
- The N‐Step Iteration Procedures
