Residual and Restarting in Krylov Subspace Evaluation of the $\varphi$ Function
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Publication:5165445
DOI10.1137/20M1375383zbMath1491.65032arXiv2010.08494OpenAlexW3209207841MaRDI QIDQ5165445
Leonid Knizhnerman, Evgenij E. Tyrtyshnikov, Mikhail A. Botchev
Publication date: 16 November 2021
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2010.08494
Krylov subspace methodsmatrix exponentialexponential time integrationrestarting\(\varphi\) matrix functionexponential residual
Numerical methods for initial value problems involving ordinary differential equations (65L05) Matrix exponential and similar functions of matrices (15A16) Numerical computation of matrix exponential and similar matrix functions (65F60)
Related Items (4)
Exponential Euler and backward Euler methods for nonlinear heat conduction problems ⋮ Coarse Grid Corrections in Krylov Subspace Evaluations of the Matrix Exponential ⋮ Inexact rational Krylov Subspace methods for approximating the action of functions of matrices ⋮ Krylov Subspace Restarting for Matrix Laplace Transforms
Uses Software
Cites Work
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- Numerical range, GMRES and Faber polynomials.
- Calculation of functions of unsymmetric matrices using Arnoldi's method
- High-order splitting schemes for semilinear evolution equations
- Krylov subspace exponential time domain solution of Maxwell's equations in photonic crystal modeling
- Evaluating matrix functions for exponential integrators via Carathéodory-Fejér approximation and contour integrals
- Implementation of a restarted Krylov subspace method for the evaluation of matrix functions
- Application of operator splitting to the Maxwell equations including a source term
- Implementation of exponential Rosenbrock-type integrators
- An iterative solution method for solving \(f(A)x=b\), using Krylov subspace information obtained for the symmetric positive definite matrix A
- A Krylov projection method for systems of ODEs
- Exponential Krylov time integration for modeling multi-frequency optical response with monochromatic sources
- Stability control for approximate implicit time stepping schemes with minimum residual iterations
- Symmetry-preserving discretization of turbulent flow.
- KIOPS: a fast adaptive Krylov subspace solver for exponential integrators
- ART: adaptive residual-time restarting for Krylov subspace matrix exponential evaluations
- Résolution numérique des grands systèmes différentiels linéaires
- The Gautschi time stepping scheme for edge finite element discretizations of the Maxwell equations
- Residual, Restarting, and Richardson Iteration for the Matrix Exponential
- Computing matrix functions
- Exponential integrators
- Efficient and Stable Arnoldi Restarts for Matrix Functions Based on Quadrature
- Algorithm 919
- Error Estimates and Evaluation of Matrix Functions via the Faber Transform
- Deflated Restarting for Matrix Functions
- Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators
- Efficient time integration for discontinuous Galerkin approximations of linear wave equations
- Iterative Solution of Linear Equations in ODE Codes
- Algorithm 866
- A New Scaling and Squaring Algorithm for the Matrix Exponential
- The Use of Iterative Linear-Equation Solvers in Codes for Large Systems of Stiff IVP<scp>s</scp> for ODE<scp>s</scp>
- Spectral Methods in Time for Parabolic Problems
- Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator
- Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
- Efficient Solution of Parabolic Equations by Krylov Approximation Methods
- Expokit
- On Krylov Subspace Approximations to the Matrix Exponential Operator
- Using Nonorthogonal Lanczos Vectors in the Computation of Matrix Functions
- Exponential Integrators for Large Systems of Differential Equations
- Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
- Inequalities for Modified Bessel Functions
- Iterative Krylov Methods for Large Linear Systems
- Krylov subspace approximation of eigenpairs and matrix functions in exact and computer arithmetic
- IFISS: A Computational Laboratory for Investigating Incompressible Flow Problems
- Convergence of Restarted Krylov Subspace Methods for Stieltjes Functions of Matrices
- Exponential Rosenbrock-Type Methods
- Solving the Maxwell equations by the Chebyshev method: a one-step finite-difference time-domain algorithm
- A Restarted Krylov Subspace Method for the Evaluation of Matrix Functions
- Functions of Matrices
- Generalized Runge-Kutta Processes for Stable Systems with Large Lipschitz Constants
- Two polynomial methods of calculating functions of symmetric matrices
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