Matrix factorizations for symplectic QR-like methods

Abstract

Symplectic QR-like methods use symplectic or unitary symplectic similarity transformations instead of the usual unitary similarity transformations in the QR process. A fundamental problem for the development of such methods is the choice of a suitable type of decomposition A = SR corresponding to the QR decomposition, where S is symplectic or unitary symplectic. Decompositions of this type are studied with regard to their application in a QR-like process.