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

Evan C. Haskell; Vehbi E. Paksoy

Special Matrices (2017)

- Volume: 5, Issue: 1, page 242-249
- ISSN: 2300-7451

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topEvan 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 -

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