Preserving geometric properties of the exponential matrix by block Krylov subspace methods (Q855288): Difference between revisions

Given a large square real matrix \(A\) and a rectangular tall matrix \(Q,\) many application problems require the approximation of the operation \(\exp (A)Q\). The authors show that an appropiate use of the block Lanczos method allows one to obtain a structure preserving approximation to \(\exp (A)Q\) when \(A\) is skew-symmetric or skew-symmetric and Hamiltonan. Moreover, for \(A\) Hamiltonian the authors derive a new variant of the block Lanczos method that again preserves the geometric properties of the exact scheme. Numerical results are also provided.