scholarly journals A Gersgorin-type lower bound for the smallest singular value

1989 ◽  
Vol 112 ◽  
pp. 1-7 ◽  
Author(s):  
Charles R. Johnson
Keyword(s):  
Lower Bound ◽  
Singular Value ◽  
Smallest Singular Value

A parameterized lower bound for the smallest singular value

2008 ◽  
Vol 17 ◽  
Author(s):  
Wei Zhang ◽  
Zheng-Zhi Han ◽  
Shu-Qian Shen
Keyword(s):  
Lower Bound ◽  
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 Schur Complement-Based Infinity Norm Bounds for the Inverse of GDSDD Matrices

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 186
Author(s):  
Yating Li ◽  
Yaqiang Wang
Keyword(s):  
Lower Bound ◽  
Schur Complement ◽  
Upper Bounds ◽  
Singular Value ◽  
Numerical Examples ◽  
Infinity Norm ◽  
Diagonally Dominant Matrices ◽  
Diagonally Dominant ◽  
Norm Bound ◽  
Smallest Singular Value

Based on the Schur complement, some upper bounds for the infinity norm of the inverse of generalized doubly strictly diagonally dominant matrices are obtained. In addition, it is shown that the new bound improves the previous bounds. Numerical examples are given to illustrate our results. By using the infinity norm bound, a lower bound for the smallest singular value is given.

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