Related papers: AE solutions and AE solvability to general interva…
Consider a linear system of equations with interval coefficients, and each interval coefficient is associated with either a universal or an existential quantifier. The AE solution set and AE solvability of the system is defined by…
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…
This paper studies the problem of testing whether a system of linear equality and inequality constraints admits a solution when the coefficients of that system may have to be estimated. We show that a wide range of inferential questions in…
Linear vector equations and inequalities are considered defined in terms of idempotent mathematics. To solve the equations, we apply an approach that is based on the analysis of distances between vectors in idempotent vector spaces. The…
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…
A quantifier-free description of the set of solutions of the generalized interval-quantifier system of linear equations is obtain.
We give improved lower bounds for the number of solutions of some $S$-unit equations over the integers, by counting the solutions of some associated linear equations as the coefficients in those equations vary over sparse sets. This method…
In this paper are examined general classes of linear and non-linear analytical systems of partial differential equations. Indeed the integrability conditions are found and if they are satisfied, the solutions are given as functional series…
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…
Presented is a new method yielding parameterized solution to an interval parametric linear system. Some properties of this method are discussed. The solution enclosure it provides is compared to the enclosures by other methods. It is shown…
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…
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…
The existence and analyticity of solutions to linear systems of moment differential equations with analytic coefficients is studied. The relation of solutions of such systems with respect to linear moment differential equations is…
We discuss the use of inequalities to obtain the solution of certain variational problems on time scales.
This work considers special types of interval linear systems - overdetermined systems. Simply said these systems have more equations than variables. The solution set of an interval linear system is a collection of all solutions of all…
We discuss various compatibility criteria for overdetermined systems of PDEs generalizing the approach to formal integrability via brackets of differential operators. Then we give sufficient conditions that guarantee that a PDE possessing a…
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…
A nonlinear inequality is formulated in the paper. An estimate of the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can be…
This paper considers the problem of testing whether there exists a solution satisfying certain non-negativity constraints to a linear system of equations. Importantly and in contrast to some prior work, we allow all parameters in the system…
Discretizations of infinite-dimensional variational inequalities lead to linear and nonlinear complementarity problems with many degrees of freedom. To solve these problems in a parallel computing environment, we propose two active-set…