Optimal Gersgorin-style estimation of the largest singular value. II

Johnson, C.R. ; Peña, J.M. (Universidad de Zaragoza) ; Szulc, T.

Resumen: In estimating the largest singular value in the class of matrices equiradial with a given $n$-by-$n$ complex matrix $A$, it was proved that it is attained at one of $n(n-1)$ sparse nonnegative matrices (see C.R.~Johnson, J.M.~Pe{\~n}a and T.~Szulc, Optimal Gersgorin-style estimation of the largest singular value; {\em Electronic Journal of Linear Algebra Algebra Appl.}, 25:48--59, 2011). Next, some circumstances were identified under which the set of possible optimizers of the largest singular value can be further narrowed (see C.R.~Johnson, T.~Szulc and D.~Wojtera-Tyrakowska, Optimal Gersgorin-style estimation of the largest singular value, {\it Electronic Journal of Linear Algebra Algebra Appl.}, 25:48--59, 2011). Here the cardinality of the mentioned set for $n$-by-$n$ matrices is further reduced. It is shown that the largest singular value, in the class of matrices equiradial with a given $n$-by-$n$ complex matrix, is attained at one of $n(n-1)/2$ sparse nonnegative matrices. Finally, an inequality between the spectral radius of a $3$-by-$3$ nonnegative matrix $X$ and the spectral radius of a modification of $X$ is also proposed.

Idioma: Inglés

DOI: 10.13001/1081-3810.3033

Año: 2016

Publicado en: Electronic Journal of Linear Algebra 31 (2016), 679-685
ISSN: 1537-9582

Factor impacto JCR: 0.475 (2016)

Categ. JCR: MATHEMATICS rank: 222 / 310 = 0.716 (2016) - Q3 - T3

Factor impacto SCIMAGO: 0.604 - Algebra and Number Theory (Q3)

Financiación: info:eu-repo/grantAgreement/ES/DGA/FSE
Financiación: info:eu-repo/grantAgreement/ES/MINECO-FEDER/MTM2015-65433-P

Tipo y forma: Article (Published version)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)