Structure-preserving methods for computing eigenpairs of large sparse skew-Hamiltonian/Hamiltonian pencils

We study large, sparse generalized eigenvalue problems for matrix pencils, where one of the matrices is Hamiltonian and the other is skew-Hamiltonian. Problems of this form arise in the numerical simulation of elastic deforma tion of anisotropic materials, in structural mechanics, and in the linear q uadratic control problem for partial differential equations. We develop a s tructure-preserving skew-Hamiltonian, isotropic, implicitly restarted shift -and-invert Arnoldi algorithm (SHIRA). Several numerical examples demonstra te the superiority of SHIRA over a competing unstructured method.