Infinity norm upper bounds for the inverse of $ SDD_1 $ matrices

Li, Yating; Liu, Liang; Wang, Yaqiang

doi:10.3934/math.2022493

Cited by 12 publications

(3 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that comparison matrix A 7 π is not the Ostrowski matrix, while, as we have already pointed out, it is a DZ matrix. However, this information is not providing a better bound, it is the same as (18), while, at the same time, required computational work is more demanding. Of course, the above example is just an illustrative one, the importance of such approach grows with the matrix dimension.…”

Section: Theorem 6 ([46]) Ifmentioning

confidence: 99%

“…For this reason, something between SDD and GDD classes, i.e., various Hmatrix subclasses, became relevant. Many such subclasses have been discovered over the years, such as doubly strictly diagonally dominant (DSDD), also known under the name Ostrowski matrices [7][8][9], Dashnic-Zusmanovich matrices [10], Dashnic-Zusmanovich type matrices [11], S-SDD or CKV matrices [12,13], CKV type matrices [14], Nekrasov matrices [15][16][17], SDD 1 matrices [18,19], etc. Various problems related to these classes have been studied, including eigenvalue localizations [2,7], pseudospectra localizations [4], infinity norm estimations of the inverse [18,[20][21][22][23][24][25][26][27], Schur complement problems [28][29][30][31], error bound for linear complementarity problems [32][33][34][35][36], etc.…”

mentioning

confidence: 99%

“…So, the natural question that immediately arises is what is the relation between these classes? Recently, in [18,19], another H-matrix subclass which treats differently SDD and non-SDD rows, has been proposed. Let N 1 (A) be the subset of indices that correspond to non-SDD rows, i.e.,…”

mentioning

confidence: 99%

See 2 more Smart Citations

On Matrices with Only One Non-SDD Row

Doroslovački

Cvetkovic

2023

Mathematics

View full text Add to dashboard Cite

The class of H-matrices, also known as Generalized Diagonally Dominant (GDD) matrices, plays an important role in many areas of applied linear algebra, as well as in a wide range of applications, such as in dynamical analysis of complex networks that arise in ecology, epidemiology, infectology, neurology, engineering, economy, opinion dynamics, and many other fields. To conclude that the particular dynamical system is (locally) stable, it is sufficient to prove that the corresponding (Jacobian) matrix is an H-matrix with negative diagonal entries. In practice, however, it is very difficult to determine whether a matrix is a non-singular H-matrix or not, so it is valuable to investigate subclasses of H-matrices which are defined by relatively simple and practical criteria. Many subclasses of H-matrices have recently been discussed in detail demonstrating the many benefits they can provide, though one particular subclass has not been fully exploited until now. The aim of this paper is to attract attention to this class and discuss its relation with other more investigated classes, while showing its main advantage, based on its simplicity and elegance. This new approach, which we are presenting in this paper, will be compared with the existing ones, in three possible areas of applications, spectrum localization; maximum norm estimation of the inverse matrix in the point, as well as the block case; and error estimation for LCP problems. The main conclusion is that the importance of our approach grows with the matrix dimension.

show abstract

Section: Theorem 6 ([46]) Ifmentioning

confidence: 99%