Open AccessA new lower bound for the smallest singular value
Author(s) -
Ksenija Doroslovački,
Ljiljana Cvetković,
Ernest Šanca
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1909711d
Subject(s) - mathematics , invertible matrix , singular value , inverse , upper and lower bounds , norm (philosophy) , singular value decomposition , matrix norm , matrix (chemical analysis) , value (mathematics) , uniform norm , combinatorics , pure mathematics , mathematical analysis , eigenvalues and eigenvectors , algorithm , geometry , statistics , physics , materials science , quantum mechanics , political science , law , composite material
The aim of this paper is to obtain new lower bounds for the smallest singular value for some special subclasses of nonsingularH-matrices. This is done in two steps: first, unifying principle for deriving new upper bounds for the norm 1 of the inverse of an arbitrary nonsingular H-matrix is presented, and then, it is combined with some well-known upper bounds for the infinity norm of the inverse. The importance and efficiency of the results are illustrated by an example from ecological modelling, as well as on a type of large-scale matrices posessing a block structure, arising in boundary value problems.