Institute of Mathematics AS CR, v. v. i.
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Inexact Newton-type method for solving large-scale absolute value equation
No full textsummary:Newton-type methods have been successfully applied to solve the absolute value equation (denoted by AVE). This class of methods usually solves a system of linear equations exactly in each iteration. However, for large-scale AVEs, solving the corresponding system exactly may be expensive. In this paper, we propose an inexact Newton-type method for solving the AVE. In each iteration, the proposed method solves the corresponding system only approximately. Moreover, it adopts a new line search technique, which is well-defined and easy to implement. We prove that the proposed method has global and local superlinear convergence under the condition that the interval matrix is regular. This condition is much weaker than those used in some Newton-type methods. Numerical results show that our method has fairly good practical efficiency for solving large-scale AVEs
A conjecture on minimum permanents
No full textsummary:We consider the permanent function on the faces of the polytope of certain doubly stochastic matrices, whose nonzero entries coincide with those of fully indecomposable square -matrices containing the identity submatrix. We show that a conjecture in K. Pula, S. Z. Song, I. M. Wanless (2011), is true for some cases by determining the minimum permanent on some faces of the polytope of doubly stochastic matrices
Representation functions for binary linear forms
No full textsummary:Let be the set of integers, the set of nonnegative integers and be a binary linear form whose coefficients , are nonzero, relatively prime integers such that and . Let be any function such that the set has asymptotic density zero. In 2007, M. B. Nathanson (2007) proved that there exists a set of integers such that for all integers , where . We add the structure of difference for the binary linear form
A balanced finite-element method for an axisymmetrically loaded thin shell
No full textsummary:We analyse a finite-element discretisation of a differential equation describing an axisymmetrically loaded thin shell. The problem is singularly perturbed when the thickness of the shell becomes small. We prove robust convergence of the method in a balanced norm that captures the layers present in the solution. Numerical results confirm our findings
Ridge estimation of covariance matrix from data in two classes
No full textsummary:This paper deals with the problem of estimating a covariance matrix from the data in two classes: (1) good data with the covariance matrix of interest and (2) contamination coming from a Gaussian distribution with a different covariance matrix. The ridge penalty is introduced to address the problem of high-dimensional challenges in estimating the covariance matrix from the two-class data model. A ridge estimator of the covariance matrix has a uniform expression and keeps positive-definite, whether the data size is larger or smaller than the data dimension. Furthermore, the ridge parameter is tuned through a cross-validation procedure. Lastly, the proposed ridge estimator is verified with better performance than the existing estimator from the data in two classes and the traditional ridge estimator only from the good data
Development of small and large compressive pulses in two-phase flow
No full textsummary:The evolutions of small and large compressive pulses are studied in a two-phase flow of gas and dust particles with a variable azimuthal velocity. The method of relatively undistorted waves is used to study the mechanical pulses of different types in a rotational, axisymmetric dusty gas. The results obtained are compared with that of nonrotating medium. Asymptotic expansion procedure is used to discuss the nonlinear theory of geometrical acoustics. The influence of the solid particles and the rotational effect of the medium on the distortion are investigated. In a rotational flow it is observed that with the increase in the value of rotational parameter, the steepening of the pulses also increases. The presence of dust in the rotational flow delays the onset of shock formation thereby increasing the distance where the shock is formed first. The rotational and the dust parameters are observed to have the same effect on the shock strength
Remark on regularity criterion for weak solutions to the shear thinning fluids
Get PDFsummary:J. Q. Yang (2019) established a regularity criterion for the 3D shear thinning fluids in the whole space via two velocity components. The goal of this short note is to extend this result in viewpoint of Lorentz space
c-ideals in complemented posets
Get PDFsummary:In their recent paper on posets with a pseudocomplementation denoted by the first and the third author introduced the concept of a -ideal. This concept is in fact an extension of a similar concept introduced in distributive pseudocomplemented lattices and semilattices by several authors, see References. Now we apply this concept of a c-ideal (dually, c-filter) to complemented posets where the complementation need neither be antitone nor an involution, but still satisfies some weak conditions. We show when an ideal or filter in such a poset is a c-ideal or c-filter, and we prove basic properties of them. Finally, we prove the so-called separation theorems for c-ideals. The text is illustrated by several examples