Summary: Regularization of linear recurrence systems \Lambda
S.A. Abramov y M. Bronstein z D.E. Khmelnov x
May 28, 2003
Abstract
We consider the problem of transforming a recurrence system
Pd(n)zn+d + Pd\Gamma1 (n)zn+d\Gamma1 + \Delta \Delta \Delta + P0(n)zn = 0
where the P i (n) are polynomial m \Theta m­matrices, into forms where the matrix Pd(n) (resp. P0(n)) is
nonsingular. As a basic auxiliary transformation we use a reduction of the system: whenever the leading
(resp. trailing) matrix is singular, then such a reduction ensures that a zero row or column appears
in it. We consider different algorithms based on different types of reduction, and show that our EG 0
reduction [2, 3] is the only two­stage reduction. We also present extensive experimental comparisons
of EG 0 with other known reductions, comparisons that confirm the practical superiority of EG 0 over
one­step reductions.
#########
############### ###### ########## ############ #######
Pd(n)zn+d + Pd\Gamma1 (n)zn+d\Gamma1 + \Delta \Delta \Delta + P0(n)zn = 0;
### ### P i (n) --- ############## m\Thetam­#######, # ####, # ####### ####### Pd(n) (##############,
P0(n)) ######## #############. # ######## ######### ################ ############## #########
######## #######: #### ####### (##############, #############) ####### #########, ## #####­
### ############ ######### # ### ####### ###### ### #######. ## ############# #########,

Source: Abramov, Sergei A. - Dorodnicyn Computing Centre of the Russian Academy of Sciences

Collections: Mathematics; Computer Technologies and Information Sciences