Sequential and parallel algebraic Riccati equations solutions via ESST on the Schur method

A method for solving the discrete/continuous algebraic Riccati equation in sequential and parallel and distributed forms, that modifies and proposes a parallelization for the Schur method of Laub (1979) is presented. To transform the symplectic/Hamiltonian matrix in a simple form, elementary stabilized similarity transformations (ESSTs) are utilized. A sequential implementation of the proposed algorithm for dense matrices is made and a parallel implementation on a distributed memory system with an asynchronous parallelization strategy over a workstations network is proposed.