On some lower bounds for smallest singular value of matrices

2021 ◽  
pp. 107411
Author(s):  
Minghua Lin ◽  
Mengyan Xie
Keyword(s):  
Lower Bounds ◽  
Singular Value ◽  
Smallest Singular Value

scholarly journals A new lower bound for the smallest singular value

Filomat ◽  
2019 ◽  
Vol 33 (9) ◽  
pp. 2711-2723
Author(s):  
Ksenija Doroslovacki ◽  
Ljiljana Cvetkovic ◽  
Ernest Sanca
Keyword(s):  
Lower Bound ◽  
Boundary Value Problems ◽  
Lower Bounds ◽  
Large Scale ◽  
Block Structure ◽  
Upper Bounds ◽  
Singular Value ◽  
Ecological Modelling ◽  
Infinity Norm ◽  
Smallest Singular Value

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.

scholarly journals Lower Bounds of the Smallest Singular Value of Matrices

2021 ◽  
Vol 13 (5) ◽  
pp. 1
Author(s):  
Liao Ping
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Singular Value ◽  
Euclidean Norm ◽  
Numerical Examples ◽  
Smallest Singular Value

In this paper, we get a lower bound of the smallest singular value of an arbitrarily matrix A by the trace of H(A) and the Euclidean norm of H(A), where H(A) is Hermitian part of A, numerical examples show the e ectiveness of our results.

scholarly journals Further lower bounds for the smallest singular value

1998 ◽  
Vol 272 (1-3) ◽  
pp. 169-179 ◽  
Author(s):  
Charles R. Johnson ◽  
Tomasz Szulc
Keyword(s):  
Lower Bounds ◽  
Singular Value ◽  
Smallest Singular Value

The block lower bounds for the smallest singular value

2005 ◽  
Vol 82 (3) ◽  
pp. 313-319 ◽  
Author(s):  
Chuan-Long Wang ◽  
Shan-Jun Zhang
Keyword(s):  
Lower Bounds ◽  
Singular Value ◽  
Smallest Singular Value
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