INVERSE SPREAD LIMIT OF A NONNEGATIVE MATRIX

For a given nonnegative n × n matrix A consider the following quantity <img border=0 width=228 height=30 src="http:/fbpe/img/proy/v29n2/img02.JPG" alt="http:/fbpe/img/proy/v29n2/img02.JPG">as long as the denominator is positive. It is simply the ratio between the smallest a...

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Autores principales:	Abueida,Atif, Nielsen,Mark, Yau Tamv,Tin
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2010
Materias:	Nonnegative matrices inverse spread evolutionary biology DNA
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172010000200004
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spelling	oai:scielo:S0716-091720100002000042014-08-14INVERSE SPREAD LIMIT OF A NONNEGATIVE MATRIXAbueida,AtifNielsen,MarkYau Tamv,Tin Nonnegative matrices inverse spread evolutionary biology DNA For a given nonnegative n × n matrix A consider the following quantity <img border=0 width=228 height=30 src="http:/fbpe/img/proy/v29n2/img02.JPG" alt="http:/fbpe/img/proy/v29n2/img02.JPG">as long as the denominator is positive. It is simply the ratio between the smallest and the largest entries of Am. We call s(Am) the inverse spread of Am which is interpreted as a measure of the maximum variation among the entries of Am in the multiplicative and reciprocal sense. Smaller s(Am) means a larger variation for Am. Clearly 0 = s(Am) = 1 for all m = 1, 2, . . . We study the asymptotic behavior of s(Am), that is, the behavior of s(Am) as m ? 8. The study arises from evolutionary biology.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.29 n.2 20102010-08-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172010000200004en10.4067/S0716-09172010000200004
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Nonnegative matrices inverse spread evolutionary biology DNA
spellingShingle	Nonnegative matrices inverse spread evolutionary biology DNA Abueida,Atif Nielsen,Mark Yau Tamv,Tin INVERSE SPREAD LIMIT OF A NONNEGATIVE MATRIX
description	For a given nonnegative n × n matrix A consider the following quantity <img border=0 width=228 height=30 src="http:/fbpe/img/proy/v29n2/img02.JPG" alt="http:/fbpe/img/proy/v29n2/img02.JPG">as long as the denominator is positive. It is simply the ratio between the smallest and the largest entries of Am. We call s(Am) the inverse spread of Am which is interpreted as a measure of the maximum variation among the entries of Am in the multiplicative and reciprocal sense. Smaller s(Am) means a larger variation for Am. Clearly 0 = s(Am) = 1 for all m = 1, 2, . . . We study the asymptotic behavior of s(Am), that is, the behavior of s(Am) as m ? 8. The study arises from evolutionary biology.
author	Abueida,Atif Nielsen,Mark Yau Tamv,Tin
author_facet	Abueida,Atif Nielsen,Mark Yau Tamv,Tin
author_sort	Abueida,Atif
title	INVERSE SPREAD LIMIT OF A NONNEGATIVE MATRIX
title_short	INVERSE SPREAD LIMIT OF A NONNEGATIVE MATRIX
title_full	INVERSE SPREAD LIMIT OF A NONNEGATIVE MATRIX
title_fullStr	INVERSE SPREAD LIMIT OF A NONNEGATIVE MATRIX
title_full_unstemmed	INVERSE SPREAD LIMIT OF A NONNEGATIVE MATRIX
title_sort	inverse spread limit of a nonnegative matrix
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2010
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172010000200004
work_keys_str_mv	AT abueidaatif inversespreadlimitofanonnegativematrix AT nielsenmark inversespreadlimitofanonnegativematrix AT yautamvtin inversespreadlimitofanonnegativematrix
_version_	1718439769170509824

INVERSE SPREAD LIMIT OF A NONNEGATIVE MATRIX

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