Spectral properties of a sequence of matrices connected to each other via Schur complement and arising in a compartmental model

Evan C. Haskell, and Vehbi E. Paksoy. "Spectral properties of a sequence of matrices connected to each other via Schur complement and arising in a compartmental model." Special Matrices 5.1 (2017): 242-249. <http://eudml.org/doc/288294>.

@article{EvanC2017,
abstract = {We consider a sequence of real matrices An which is characterized by the rule that An−1 is the Schur complement in An of the (1,1) entry of An, namely −en, where en is a positive real number. This sequence is closely related to linear compartmental ordinary differential equations. We study the spectrum of An. In particular,we show that An has a unique positive eigenvalue λn and \{λn\} is a decreasing convergent sequence. We also study the stability of An for small n using the Routh-Hurwitz criterion.},
author = {Evan C. Haskell, Vehbi E. Paksoy},
journal = {Special Matrices},
keywords = {Schur complement; Routh-Hurwitz criterion; elementary symmetric polynomials; linear compartmental model; latency phase},
language = {eng},
number = {1},
pages = {242-249},
title = {Spectral properties of a sequence of matrices connected to each other via Schur complement and arising in a compartmental model},
url = {http://eudml.org/doc/288294},
volume = {5},
year = {2017},
}

TY - JOUR
AU - Evan C. Haskell
AU - Vehbi E. Paksoy
TI - Spectral properties of a sequence of matrices connected to each other via Schur complement and arising in a compartmental model
JO - Special Matrices
PY - 2017
VL - 5
IS - 1
SP - 242
EP - 249
AB - We consider a sequence of real matrices An which is characterized by the rule that An−1 is the Schur complement in An of the (1,1) entry of An, namely −en, where en is a positive real number. This sequence is closely related to linear compartmental ordinary differential equations. We study the spectrum of An. In particular,we show that An has a unique positive eigenvalue λn and {λn} is a decreasing convergent sequence. We also study the stability of An for small n using the Routh-Hurwitz criterion.
LA - eng
KW - Schur complement; Routh-Hurwitz criterion; elementary symmetric polynomials; linear compartmental model; latency phase
UR - http://eudml.org/doc/288294
ER -