Expokit: a software package for computing matrix exponentials
ACM Transactions on Mathematical Software (TOMS)
Krylov Subspaces and Electromagnetic Oil Exploration
IEEE Computational Science & Engineering
Complexity theory for lie-group solvers
Journal of Complexity
Applied Mathematics and Computation
A polynomial method based on Fejèr points for the computation of functions of unsymmetric matrices
Applied Numerical Mathematics
Computing a matrix function for exponential integrators
Journal of Computational and Applied Mathematics
A variational splitting integrator for quantum molecular dynamics
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Interpolating discrete advection-diffusion propagators at Leja sequences
Journal of Computational and Applied Mathematics
The Gautschi time stepping scheme for edge finite element discretizations of the Maxwell equations
Journal of Computational Physics
Dual diffusion model of spreading activation for content-based image retrieval
MIR '06 Proceedings of the 8th ACM international workshop on Multimedia information retrieval
EXPINT---A MATLAB package for exponential integrators
ACM Transactions on Mathematical Software (TOMS)
Exponential Runge-Kutta methods for parabolic problems
Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
Journal of Computational Physics
An error analysis of the modified scaling and squaring method
Computers & Mathematics with Applications
Practical Implementation of Krylov Subspace Spectral Methods
Journal of Scientific Computing
On the construction of restricted-denominator exponential W-methods
Journal of Computational and Applied Mathematics
A rational Krylov method for solving time-periodic differential equations
Applied Numerical Mathematics
Journal of Computational Physics
Exponential time integration and Chebychev discretisation schemes for fast pricing of options
Applied Numerical Mathematics
Graph spectral image smoothing using the heat kernel
Pattern Recognition
Probabilistic relaxation labelling using the Fokker-Planck equation
Pattern Recognition
Approximation of matrix operators applied to multiple vectors
Mathematics and Computers in Simulation
Parallel solution in time of ODEs: some achievements and perspectives
Applied Numerical Mathematics
Application of operator splitting to the Maxwell equations including a source term
Applied Numerical Mathematics
Implementation of exponential Rosenbrock-type integrators
Applied Numerical Mathematics
Error Bounds for Lanczos Approximations of Rational Functions of Matrices
Numerical Validation in Current Hardware Architectures
A massively parallel exponential integrator for advection-diffusion models
Journal of Computational and Applied Mathematics
Exponential Runge--Kutta methods for parabolic problems
Applied Numerical Mathematics
A second-order Magnus-type integrator for nonautonomous parabolic problems
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
An exponential integrator for advection-dominated reactive transport in heterogeneous porous media
Journal of Computational Physics
A quick rank based on web structure
PRICAI'06 Proceedings of the 9th Pacific Rim international conference on Artificial intelligence
A survey on methods for computing matrix exponentials in numerical schemes for ODEs
ICCS'03 Proceedings of the 2003 international conference on Computational science: PartII
ICCS'03 Proceedings of the 2003 international conference on Computational science: PartIII
Journal of Computational Physics
A multi-resolution approach to heat kernels on discrete surfaces
ACM SIGGRAPH 2010 papers
Model checking Markov chains using Krylov subspace methods: an experience report
EPEW'10 Proceedings of the 7th European performance engineering conference on Computer performance engineering
Symplectic and multisymplectic numerical methods for Maxwell's equations
Journal of Computational Physics
On the use of matrix functions for fractional partial differential equations
Mathematics and Computers in Simulation
Approximation of Semigroups and Related Operator Functions by Resolvent Series
SIAM Journal on Numerical Analysis
Shift-Invert Arnoldi Approximation to the Toeplitz Matrix Exponential
SIAM Journal on Scientific Computing
Semi-Lagrangian multistep exponential integrators for index 2 differential-algebraic systems
Journal of Computational Physics
High-order commutator-free exponential time-propagation of driven quantum systems
Journal of Computational Physics
A new class of exponential propagation iterative methods of Runge-Kutta type (EPIRK)
Journal of Computational Physics
Computing $f(A)b$ via Least Squares Polynomial Approximations
SIAM Journal on Scientific Computing
Approximating Semidefinite Packing Programs
SIAM Journal on Optimization
Novel Numerical Methods for Solving the Time-Space Fractional Diffusion Equation in Two Dimensions
SIAM Journal on Scientific Computing
Dimensional Reductions for the Computation of Time-Dependent Quantum Expectations
SIAM Journal on Scientific Computing
On the Convergence of Krylov Subspace Methods for Matrix Mittag-Leffler Functions
SIAM Journal on Numerical Analysis
Journal of Computational and Applied Mathematics
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
ACM Transactions on Mathematical Software (TOMS)
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
A structure preserving approximation method for Hamiltonian exponential matrices
Applied Numerical Mathematics
Using the Restricted-denominator Rational Arnoldi Method for Exponential Integrators
SIAM Journal on Matrix Analysis and Applications
Computation of matrix functions with deflated restarting
Journal of Computational and Applied Mathematics
Comparative performance of exponential, implicit, and explicit integrators for stiff systems of ODEs
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Circuit simulation via matrix exponential method for stiffness handling and parallel processing
Proceedings of the International Conference on Computer-Aided Design
Exponential Taylor methods: Analysis and implementation
Computers & Mathematics with Applications
Locally exact modifications of numerical schemes
Computers & Mathematics with Applications
Exponential integrators for stiff elastodynamic problems
ACM Transactions on Graphics (TOG)
Exponential Rosenbrock methods of order five - construction, analysis and numerical comparisons
Journal of Computational and Applied Mathematics
Improving the accuracy of the AVF method
Journal of Computational and Applied Mathematics
Approximation of the matrix exponential operator by a structure-preserving block Arnoldi-type method
Applied Numerical Mathematics
Journal of Scientific Computing
Array-representation integration factor method for high-dimensional systems
Journal of Computational Physics
Journal of Computational Physics
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Krylov subspace methods for approximating the action of matrix exponentials are analyzed in this paper. We derive error bounds via a functional calculus of Arnoldi and Lanczos methods that reduces the study of Krylov subspace approximations of functions of matrices to that of linear systems of equations. As a side result, we obtain error bounds for Galerkin-type Krylov methods for linear equations, namely, the biconjugate gradient method and the full orthogonalization method. For Krylov approximations to matrix exponentials, we show superlinear error decay from relatively small iteration numbers onwards, depending on the geometry of the numerical range, the spectrum, or the pseudospectrum. The convergence to exp$(\tau A)v$ is faster than that of corresponding Krylov methods for the solution of linear equations $(I-\tau A)x=v$, which usually arise in the numerical solution of stiff ordinary differential equations (ODEs). We therefore propose a new class of time integration methods for large systems of nonlinear differential equations which use Krylov approximations to the exponential function of the Jacobian instead of solving linear or nonlinear systems of equations in every time step.