Towards understanding CG and GMRES through examples (Q6496390)

scientific article; zbMATH DE number 7842029

Language	Label	Description	Also known as
English	Towards understanding CG and GMRES through examples	scientific article; zbMATH DE number 7842029

Statements

instance of

scholarly article

0 references

title

Towards understanding CG and GMRES through examples (English)

0 references

0 references

0 references

0 references

Linear Algebra and its Applications

0 references

publication date

3 May 2024

0 references

zbMATH Keywords

Krylov subspace methods

0 references

method of moments

0 references

CG method

0 references

GMRES method

0 references

iterative methods

0 references

convergence analysis

0 references

rounding error analysis

0 references

polynomial approximation problems

0 references

MaRDI profile type

MaRDI publication profile

0 references

cites work

Krylov sequences of maximal length and convergence of GMRES

0 references

The principle of minimized iterations in the solution of the matrix eigenvalue problem

0 references

A Taxonomy for Conjugate Gradient Methods

0 references

Preconditioning techniques for large linear systems: A survey

0 references

The methods of Vorobyev and Lanczos

0 references

On the cost of iterative computations

0 references

The Numerical Stability Analysis of Pipelined Conjugate Gradient Methods: Historical Context and Methodology

0 references

Computing Spectral Measures of Self-Adjoint Operators

0 references

Use of Fast Direct Methods for the Efficient Numerical Solution of Nonseparable Elliptic Equations

0 references

Analyzing the Effect of Local Rounding Error Propagation on the Maximal Attainable Accuracy of the Pipelined Conjugate Gradient Method

0 references

Numerical stability of GMRES

0 references

Krylov subspace approximation of eigenpairs and matrix functions in exact and computer arithmetic

0 references

On investigating GMRES convergence using unitary matrices

0 references

The probability that a random real Gaussian matrix has \(k\) real eigenvalues, related distributions, and the circular law

0 references

IFISS: A Computational Laboratory for Investigating Incompressible Flow Problems

0 references

Finite Elements and Fast Iterative Solvers

0 references

The Tortoise and the Hare Restart GMRES

0 references

Minimal Residual Method Stronger than Polynomial Preconditioning

0 references

Properties of Worst-Case GMRES

0 references

On the theory of equivalent operators and application to the numerical solution of uniformly elliptic partial differential equations

0 references

Q4091368

0 references

Solving linear algebraic equations can be interesting

0 references

Q4016503

0 references

QMR: A quasi-minimal residual method for non-Hermitian linear systems

0 references

Laplacian Preconditioning of Elliptic PDEs: Localization of the Eigenvalues of the Discretized Operator

0 references

Numerical approximation of the spectrum of self-adjoint operators in operator preconditioning

0 references

Rounding error analysis of the classical Gram-Schmidt orthogonalization process

0 references

Matrices, moments and quadrature. II: How to compute the norm of the error iterative methods

0 references

Some History of the Conjugate Gradient and Lanczos Algorithms: 1948–1976

0 references

Estimates in quadratic formulas

0 references

Q4358701

0 references

Chebyshev semi-iterative methods, successive overrelaxation iterative methods, and second order Richardson iterative methods. I, II

0 references

Calculation of Gauss Quadrature Rules

0 references

Error Bounds in Equilibrium Statistical Mechanics

0 references

Matrix interpretations and applications of the continued fraction algorithm

0 references

Comparison of splittings used with the conjugate gradient algorithm

0 references

Behavior of slightly perturbed Lanczos and conjugate-gradient recurrences

0 references

Q4348514

0 references

Max-Min Properties of Matrix Factor Norms

0 references

Any Nonincreasing Convergence Curve is Possible for GMRES

0 references

Predicting the Behavior of Finite Precision Lanczos and Conjugate Gradient Computations

0 references

Q4309410

0 references

GMRES/CR and Arnoldi/Lanczos as Matrix Approximation Problems

0 references

Accuracy of Two Three-term and Three Two-term Recurrences for Krylov Space Solvers

0 references

Iterative solution of large sparse systems of equations. Transl. from the German

0 references

Methods of conjugate gradients for solving linear systems

0 references

Decomposition into subspaces preconditioning: abstract framework

0 references

Influence of the Eigenvalue Spectrum on the Convergence Rate of the Conjugate Gradient Method

0 references

A Robust GMRES-Based Adaptive Polynomial Preconditioning Algorithm for Nonsymmetric Linear Systems

0 references

Convergence of a Method of Solving Linear Problems

0 references

Which Eigenvalues Are Found by the Lanczos Method?

0 references

An optimal preconditioned FFT-accelerated finite element solver for homogenization

0 references

Guaranteed two-sided bounds on all eigenvalues of preconditioned diffusion and elasticity problems solved by the finite element method.

0 references

Elimination of ringing artifacts by finite-element projection in FFT-based homogenization

0 references

GMRES Convergence Analysis for a Convection-Diffusion Model Problem

0 references

Q4649579

0 references

Convergence analysis of Krylov subspace methods

0 references

Max-min and min-max approximation problems for normal matrices revisited

0 references

Approximating Spectral Densities of Large Matrices

0 references

Q4333658

0 references

Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs

0 references

The Lanczos and Conjugate Gradient Algorithms

0 references

On prescribing the convergence behavior of the conjugate gradient algorithm

0 references

Krylov Methods for Nonsymmetric Linear Systems

0 references

Accurate error estimation in CG

0 references

The Lanczos and conjugate gradient algorithms in finite precision arithmetic

0 references

Convergence of Adaptive Finite Element Methods

0 references

A Note on Preconditioning for Indefinite Linear Systems

0 references

Preconditioning by inverting the Laplacian: an analysis of the eigenvalues

0 references

On the convergence rate of the conjugate gradients in presence of rounding errors

0 references

Accuracy and effectiveness of the Lanczos algorithm for the symmetric eigenproblem

0 references

Modified Gram-Schmidt (MGS), Least Squares, and Backward Stability of MGS-GMRES

0 references

Solution of Sparse Indefinite Systems of Linear Equations

0 references

Bounds for the least squares distance using scaled total least squares

0 references

Residual and Backward Error Bounds in Minimum Residual Krylov Subspace Methods

0 references

Two‐sided guaranteed bounds to individual eigenvalues of preconditioned finite element and finite difference problems

0 references

Eigenvalues and pseudo-eigenvalues of Toeplitz matrices

0 references

On the Compatibility of a Given Solution With the Data of a Linear System

0 references

Krylov Subspace Methods for Solving Large Unsymmetric Linear Systems

0 references

Q4414854

0 references

GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems

0 references

On the real convergence rate of the conjugate gradient method

0 references

Model reduction using the Vorobyev moment problem

0 references

On error estimation in the conjugate gradient method and why it works in finite precision computations

0 references

Error estimation in preconditioned conjugate gradients

0 references

GMRES vs. Ideal GMRES

0 references

Q4288951

0 references

Q4337625

0 references

Q5694789

0 references

The rate of convergence of conjugate gradients

0 references

Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems

0 references

Iterative Krylov Methods for Large Linear Systems

0 references

0 references

0 references

0 references

0 references

Identifiers

Mathematics Subject Classification ID

0 references

0 references

0 references

0 references

10.1016/J.LAA.2024.04.003

0 references

Sitelinks

Mathematics(1 entry)

mardi Publication:6496390