Analysis of some Krylov subspace approximations to the matrix exponential operator
SIAM Journal on Numerical Analysis
A Krylov projection method for systems of ODEs
Selected papers of the second international conference on Numerical solution of Volterra and delay equations : Volterra centennial: Volterra centennial
On Krylov Subspace Approximations to the Matrix Exponential Operator
SIAM Journal on Numerical Analysis
The Geometry of Algorithms with Orthogonality Constraints
SIAM Journal on Matrix Analysis and Applications
Computation of the Exponential of Large Sparse Skew-Symmetric Matrices
SIAM Journal on Scientific Computing
A structure preserving approximation method for Hamiltonian exponential matrices
Applied Numerical Mathematics
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The approximation of exp(A)V, where A is a real matrix and V a rectangular matrix, is the key ingredient of many exponential integrators for solving systems of ordinary differential equations. The use of Krylov subspace techniques in this context has been actively investigated; see Calledoni and Moret (1997) [10], Hochbruck and Lubich (1997) [17], Saad (1992) [20]. An appropriate structure preserving block method for approximating exp(A)V, where A is a large square real matrix and V a rectangular matrix, is given in Lopez and Simoncini (2006) [18]. A symplectic Krylov method to approximate exp(A)V was also proposed in Agoujil et al. (2012) [2] with V@?R^2^n^x^2. The purpose of this work is to describe a structure preserving block Krylov method for approximating exp(A)V when A is a Hamiltonian or skew-Hamiltonian 2n-by-2n real matrix and V is a 2n-by-2s matrix (s@?n). Our approach is based on block Krylov subspace methods that preserve Hamiltonian and skew-Hamiltonian structures.