Combining the Skew-Hamiltonian Isotropic implicitly Restarted Arnoldi algorithm (SHIRA) due to Mehrmann and Waktins and the refined projection principle proposed by the first author, we present a Skew-Hamiltonian Isotropic implicitly Restarted Refined Arnoldi algorithm (SHIRRA) for the skew-Hamiltonian/Hamiltonian (SHH) pencil eigenvalue problem. Within SHIRRA, we propose new shifts, called refined shifts, that are theoretically better and numerically more efficient than the exact shifts used within SHIRA. Numerical examples illustrate the efficiency and superiority of SHIRRA.
"SHIRRA: A REFINED VARIANT OF SHIRA FOR THE SKEW-HAMILTONIAN/HAMILTONIAN (SHH) PENCIL EIGENVALUE PROBLEM." Taiwanese J. Math. 17 (1) 259 - 274, 2013. https://doi.org/10.11650/tjm.17.2013.1949