Numerical methods for ordinary differential equations on matrix manifolds
Journal of Computational and Applied Mathematics
Computation of functions of Hamiltonian and skew-symmetric matrices
Mathematics and Computers in Simulation
On the solution of skew-symmetric shifted linear systems
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part IV
Partial retrieval of CAD models based on the gradient flows in Lie group
Pattern Recognition
A structure preserving approximation method for Hamiltonian exponential matrices
Applied Numerical Mathematics
Approximation of the matrix exponential operator by a structure-preserving block Arnoldi-type method
Applied Numerical Mathematics
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In this paper we consider methods for evaluating both exp(A) and $exp(\tau A)q_1$ where ${\rm exp}(\cdot)$ is the exponential function, A is a sparse skew-symmetric matrix of large dimension, q1 is a given vector, and $\tau$ is a scaling factor. The proposed method is based on two main steps: A is factorized into its tridiagonal form H by the well-known Lanczos iterative process, and then exp(A) is derived making use of an effective Schur decomposition of H. The procedure takes full advantage of the sparsity of A and of the decay behavior of exp(H). Several applications and numerical tests are also reported.