A standard symplectic structure arises naturally in the discrete algebraic Riccati equations. This note contains two results. First, by means of a parameter representation it is shown that the set of all 2n × 2n standard symplectic matrices is closed undermultiplication and, thus, forms a semigroup. Secondly, block LU-decompositions of powers of the involved matrix can be derived in closed form which, in turn, can be employed recursively to induce an effective structure-preserving algorithm for solving the Riccati equations. The computational cost of doubling and tripling of the powers is investigated. It is concluded that doubling is the better strategy.
On the semigroup of standard symplectic matrices and its applications
RAGNI, Stefania
2004
Abstract
A standard symplectic structure arises naturally in the discrete algebraic Riccati equations. This note contains two results. First, by means of a parameter representation it is shown that the set of all 2n × 2n standard symplectic matrices is closed undermultiplication and, thus, forms a semigroup. Secondly, block LU-decompositions of powers of the involved matrix can be derived in closed form which, in turn, can be employed recursively to induce an effective structure-preserving algorithm for solving the Riccati equations. The computational cost of doubling and tripling of the powers is investigated. It is concluded that doubling is the better strategy.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
