Related papers: Solution of linear equations and inequalities in i…
We study some examples when there is actually an equality in the linear algebra bound. When the vectors considered span in fact the entire space. We would like to point out that in some cases this provides some interesting extra information…
This paper describes infinite sets of polynomial equations in infinitely many variables with the property that the existence of a solution or even an approximate solution for every finite subset of the equations implies the existence of a…
In this paper, we generalize the classical extragradient algorithm for solving variational inequality problems by utilizing nonzero normal vectors of the feasible set. In particular, conceptual algorithms are proposed with two different…
The displacement and deviation vectors in spaces (manifolds), the tangent bundle of which is endowed with a transport along paths, are introduced. In case these spaces are equipped with a linear connection, the deviation equations (between…
Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…
Multidimensional minimax single facility location problems with Chebyshev distance are examined within the framework of idempotent algebra. A new algebraic solution based on an extremal property of the eigenvalues of irreducible matrices is…
Let A be an m-dimensional vector with positive real entries. Let A_{i,j} be the vector obtained from A on deleting the entries A_i and A_j. We investigate some invariant and near invariants related to the solutions E (m-2 dimensional…
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
The paper focuses on a multidimensional optimization problem, which is formulated in terms of tropical mathematics and consists in minimizing a nonlinear objective function subject to linear inequality constraints. To solve the problem, we…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
We present a general formula for the particular solution of an inhomogeneous linear difference equation with variable coefficients. The answer is expressed as a weighted sum of fundamental solutions of the associated linear difference…
Direct solution of simultaneous linear equations is regarded to be slow for large systems of equations and requires special treatment to avoid numerical instability. A new method is proposed that addresses the numerical instability without…
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 consider a constrained minimax single facility location problem on the plane with rectilinear distance. The feasible set of location points is restricted to rectangles with sides oriented at a 45 degrees angle to the axes of Cartesian…
The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…
Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential…
A convergent iterative process is constructed for solving any solvable linear equation in a Hilbert space.
We prove existence and uniqueness of a solution to the problem of minimizing the logarithmic energy of vector potentials associated to a $d$-tuple of positive measures supported on closed subsets of the complex plane. The assumptions we…
This paper is based on my talk at ICM on recent progress in a number of classical problems of linear algebra and representation theory, based on new approach, originated from geometry of stable bundles and geometric invariant theory.
This paper studies approximate solutions of a linear fractional vector optimization problem without requiring boundedness of the constraint set. We establish necessary and sufficient conditions for approximating weakly efficient points of…