Numerical Solution of Quadratic Eigenvalue Problems with Structure-Preserving Methods
Tsung‐Min Hwang, Wen‐Wei Lin, Volker Mehrmann · SIAM Journal on Scientific Computing · 2003
Numerical methods for the solution of large scale structured quadratic eigenvalue problems are discussed. We describe a new extraction procedure for the computation of eigenvectors and invariant subspaces of skew-Hamiltonian/Hamiltonian pencils using the recently proposed skew-Hamiltonian isotropic implicitly restarted Arnoldi method (SHIRA). As an application we discuss damped gyroscopic systems. For this problem we first solve the eigenvalue problem for the undamped system using the structure-preserving method and then use the quadratic Jacobi--Davidson method as correction procedure. We also illustrate the properties of the new approach for several other application problems.