Abstract
A matrix Z ? R2n×2n is said to be in the standard symplectic form if Z enjoys a block
LU-decomposition in the sense of
A 0
-H I
Z =
I G
0 AT
, where A is nonsingular and both
G and H are symmetric and positive definite in Rn×n. Such a 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 Z 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.
Anno
2004
Autori IAC
Tipo pubblicazione
Altri Autori
Chu M.T.; Del Buono N.; Diele F.; Politi T.; Ragni S.
Editore
North Holland [etc.]
Rivista
Linear algebra and its applications