Chu, DelinLiu, XinminMehrmann, Volker2021-12-172021-12-172004-10-042197-8085https://depositonce.tu-berlin.de/handle/11303/15530http://dx.doi.org/10.14279/depositonce-14303In this paper we solve a long-standing open problem in numerical analysis called 'Van Loan's Curse'. We derive a new numerical method for computing the Hamiltonian Schur form of a Hamiltonian matrix that has no purely imaginary eigenvalues. The proposed method is numerically strongly backward stable, i.e., it computes the exact Hamiltonian Schur form of a nearby Hamiltonian matrix, and it is of complexity O(n^3) and thus Van Loan's curse is lifted. We demonstrate the quality of the new method by showing its performance for the benchmark collection of continuous-time algebraic Riccati equations.en510 MathematikHamiltonian matrixskew-Hamiltonian matrixreal Hamiltonian Schur formreal skew-Hamiltonian Schur formsymplectic URV-decompositionstable invariant subspaceResearch Paper