Numerical methods for ordinary differential equations on matrix manifolds
Journal of Computational and Applied Mathematics
On a new iterative method for solving linear systems and comparison results
Journal of Computational and Applied Mathematics
Approximation of matrix operators applied to multiple vectors
Mathematics and Computers in Simulation
Error Bounds for Lanczos Approximations of Rational Functions of Matrices
Numerical Validation in Current Hardware Architectures
On the use of matrix functions for fractional partial differential equations
Mathematics and Computers in Simulation
On Analysis of Projection Methods for Rational Function Approximation to the Matrix Exponential
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
Novel Numerical Methods for Solving the Time-Space Fractional Diffusion Equation in Two Dimensions
SIAM Journal on Scientific Computing
On the Convergence of Krylov Subspace Methods for Matrix Mittag-Leffler Functions
SIAM Journal on Numerical Analysis
Schur decomposition methods for the computation of rational matrix functions
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part IV
Computation of matrix functions with deflated restarting
Journal of Computational and Applied Mathematics
A family of Adams exponential integrators for fractional linear systems
Computers & Mathematics with Applications
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Krylov subspace methods for approximating the action of the matrix exponential exp(A) on a vector v are analyzed with A Hermitian and negative semidefinite. Our approach is based on approximating the exponential with the commonly employed diagonal Padé and Chebyshev rational functions, which yield a system of equations with a polynomial coefficient matrix. We derive optimality properties and error bounds for the convergence of a Galerkin-type approximation and of a computationally feasible and extensively used alternative. As complementary results, we theoretically justify the use of a popular a posteriori error estimate, and we provide upper bounds for the components of the solution vector. Our theoretical and numerical results show that this methodology may provide an appropriate framework to devise new strategies such as more powerful acceleration schemes.