Related papers: AE regularity of interval matrices
We consider linear systems of equations and inequalities with coefficients varying inside given intervals. We define their solutions (so called AE solutions) and solvability (so called AE solvability) by using forall-exists quantification…
We consider a system of linear equations, whose coefficients depend linearly on interval parameters. Its solution set is defined as the set of all solutions of all admissible realizations of the parameters. We study unbounded directions of…
Matrix regularity is a key to various problems in applied mathematics. The sufficient conditions, used for checking regularity of interval parametric matrices, usually fail in case of large parameter intervals. We present necessary and…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
We consider the linear complementarity problem with uncertain data modeled by intervals, representing the range of possible values. Many properties of the linear complementarity problem (such as solvability, uniqueness, convexity, finite…
This paper provides an overview of the necessary and sufficient conditions for guaranteeing the unique solvability of absolute value equations. In addition to discussing the basic form of these equations, we also address several…
We analyze different approaches to differential-algebraic equations with attention to the implemented rank conditions of various matrix functions. These conditions are apparently very different and certain rank drops in some matrix…
The concepts of differentiation and integration for matrices are known. As far as each matrix is differentiable, it is not clear a priori whether a given matrix is integrable or not. Recently some progress was obtained for diagonalizable…
As AI systems develop in complexity it is becoming increasingly hard to ensure non-discrimination on the basis of protected attributes such as gender, age, and race. Many recent methods have been developed for dealing with this issue as…
In various applications the search for certificates for certain properties (e.g., stability of dynamical systems, program termination) can be formulated as a quantified constraint solving problem with quantifier prefix exists-forall. In…
In this paper, we consider the solution of ill-conditioned systems of linear algebraic equations that can be determined imprecisely. To improve the stability of the solution process, we "immerse" the original imprecise linear system in an…
Interval systems of linear algebraic equations (ISLAE) are considered in the context of constructing of linear models according to data with interval uncertainty. Sufficient conditions for boundedness and convexity of an admissible domain…
This paper studies the concept of algorithmic equiresolution of a family of embedded varieties or ideals, which means a simultaneous resolution of such a family compatible with a given (suitable) algorithm of resolution in characteristic…
Let $A$ be a $n\times n$ real matrix. The piecewise linear equation system $z-A\vert z\vert =b$ is called an absolute value equation (AVE). It is well-known to be equivalent to the linear complementarity problem. Unique solvability of the…
The absolute value equations (AVE) problem is an algebraic problem of solving Ax+|x|=b. So far, most of the research focused on methods for solving AVEs, but we address the problem itself by analysing properties of AVE and the corresponding…
An interval matrix is a matrix whose entries are intervals in the set of real numbers. We generalize this concept, which has been broadly studied, to other fields. Precisely we define a rational interval matrix to be a matrix whose entries…
We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of…
Ioffe's criterion and various reformulations of it have become a~standard tool in proving theorems guaranteeing various regularity properties such as metric regularity, i.e., the openness with a linear rate around the reference point, of…
The solvability and stability analysis of linear time invariant systems of delay differential-algebraic equations (DDAEs) is analyzed. The behavior approach is applied to DDAEs in order to establish characterizations of their solvability in…
Devising a fair classifier that does not discriminate against different groups is an important problem in machine learning. Although researchers have proposed various ways of defining group fairness, most of them only focused on the…