In this paper we consider methods for evaluating both exp(A) and exp(τA)q1 where exp(·) is the exponential function, A is a sparse skew-symmetric matrix of large dimension, q1 is a given vector, and τ 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.
Computation of Exponentials of Large Sparse Skew Symmetric Matrices
DEL BUONO, Nicoletta;LOPEZ, Luciano;
2005-01-01
Abstract
In this paper we consider methods for evaluating both exp(A) and exp(τA)q1 where exp(·) is the exponential function, A is a sparse skew-symmetric matrix of large dimension, q1 is a given vector, and τ 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.File in questo prodotto:
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