An upper bound for the infinity norm for the inverse of Dashnic–Zusmanovich type matrices is given. It is proved that the upper bound is sharper than the well-known Varah's bound for strictly ...diagonally dominant matrices. By introducing a new subclass of P-matrices: Dashnic–Zusmanovich type B-matrices (DZ-type-B-matrices), and using the proposed infinity norm bound, an error bound is given for the linear complementarity problems of DZ-type-B-matrices. We also give a new pseudospectra localization to measure the distance to instability.
CKV-type matrices with applications Cvetković, Dragana Lj; Cvetković, Ljiljana; Li, Chaoqian
Linear algebra and its applications,
01/2021, Letnik:
608
Journal Article
Recenzirano
Several applied linear algebra research areas, such as eigenvalue localizations, infinity norm estimations for matrix inverse, pseudospectra localizations, etc., are closely connected with special ...subclasses of nonsingular H-matrices. Many of them have already been investigated in details, but it seems that finding new such subclasses is far from completed. For example, in 22, interchanging the quantifiers in the definition of the Dashnic-Zusmanovich matrices, led to a new class, benefits of which was shown in 22, 13, 11. In this paper we will apply similar idea to CKV class (also known in the literature under the name Σ-SDD class), and show several benefits from the obtained new class, which we will call CKV-type matrices.
The Schur complement of PH−matrices Nedović, Maja; Cvetković, Ljiljana
Applied mathematics and computation,
12/2019, Letnik:
362
Journal Article
Recenzirano
In this paper, we consider the class of PH−matrices, a subclass of H−matrices and, using scaling characterization, we show that this class is closed under taking the Schur complement. We show that, ...under certain conditions, the Perron complement of a PH−matrix is a PH−matrix. We also present a way of constructing a scaling matrix for the given PH−matrix and we give eigenvalue localization for the Schur complement of a PH−matrix using only the entries of the original matrix. We illustrate this by numerical examples.
It is well-known that for a given H-matrix A there exists a diagonal nonsingular matrix that scales A (by multiplying it from the right) to a strictly diagonally dominant (SDD) matrix. There are ...subclasses of H-matrices that can be fully characterised by the form of the corresponding diagonal scaling matrices. However, for some applications, it is not necessary to have such full characterisation. It is sufficient to find at least one scaling matrix that will do the job. The aim of this paper is to present a way of constructing a diagonal scaling matrix for one special subclass of H-matrices called Partition-Nekrasov matrices. As an application of this scaling approach, we obtain eigenvalue localisation for the corresponding Schur complement matrix, using only the entries of the original matrix.
B lymphocytes, as a central part of adaptive immune responses, have the ability to fight against an almost unlimited numbers of pathogens. Impairment of B cell development, activation and ...differentiation to antibody secreting plasma cells can lead to malignancy, allergy, autoimmunity and immunodeficiency. However, the impact of environmental factors, such as hyperosmolality or osmotic stress caused by varying salt concentrations in different lymphoid organs, on these processes is not well-understood. Here, we report that B cells respond to osmotic stress in a biphasic manner. Initially, increased osmolality boosted B cell activation and differentiation as shown by an untimely downregulation of Pax5 as well as upregulation of CD138. However, in the second phase, we observed an increase in cell death and impaired plasmablast differentiation. Osmotic stress resulted in impaired class switch to IgG1, inhibition of phosphorylation of p38 mitogen-activated kinase and a delayed NFAT5 response. Overall, these findings demonstrate the importance of microenvironmental hyperosmolality and osmotic stress caused by NaCl for B cell activation and differentiation.
From the application point of view, it is important to have a good upper bound for the maximum norm of the inverse of a given matrix A. In this paper we will give two simple and practical upper ...bounds for the maximum norm of the inverse of a Nekrasov matrix.
Maximum norm bound of the inverse of a given matrix is an important issue in a wide range of applications. Motivated by this fact, we will extend the list of matrix classes for which upper bounds for ...max norms can be obtained. These classes are subclasses of block H-matrices, and they stand in a general position with corresponding point-wise classes. Efficiency of new results will be illustrated by numerical examples.
The eigenvalue localization problem is very closely related to the -matrix theory. The most elegant example of this relation is the equivalence between the Geršgorin theorem and the theorem about ...nonsingularity of SDD (strictly diagonally dominant) matrices, which is a starting point for further beautiful results in the book of Varga 19. Furthermore, the corresponding Geršgorin-type theorem is equivalent to the statement that each matrix from a particular subclass of -matrices is nonsingular. Finally, the statement that all eigenvalues of a given matrix belong to minimal Geršgorin set (defined in 19) is equivalent to the statement that every -matrix is nonsingular. Since minimal Geršgorin set remained unattainable, a lot of different Geršgorin-type areas for eigenvalues has been developed recently. Along with them, a lot of new subclasses of -matrices were obtained. A survey of recent results in both areas, as well as their relationships, will be presented in this paper.
Motivated by the growing successful use of fractional differential equations in the modeling of different important phenomena, in this paper we derive tools for practical analysis of the robust ...asymptotic stability of a (incommensurate) fractional order linear system. First, the concept of fractional pseudospectra is introduced. Second, driven by the simplicity and usefulness of spectral localizations in the analysis of various matrix properties, we introduce adequate localization techniques using the ideas that come from diagonally dominant matrices, in order to localize the fractional pseudospectra. In such way, many theoretical and practical applications of pseudospectra (robust stability, transient behavior, nonnormal dynamics, etc.) in fractional order differential systems can be linked to the specificity of the matrix entries, allowing one to understand certain phenomena in practice better. Third, we consider the fractional distance to instability in ℓ∞, ℓ1 and ℓ2 norms, and determine efficient lower bounds. Finally, this novel approach is implemented on the realistic model of empirical food web to link the stability (that incorporates hereditary dynamics of living organisms) with the empirical data and their uncertainty limitations.
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