Related papers: Algorithms for Solving Linear Congruences and Syst…

This paper addresses the problem of determining the symmetries of a plane or space curve defined by a rational parametrization. We provide effective methods to compute the involution and rotation symmetries for the planar case. As for space…

We present in this paper our solver for logic grid puzzles. The approach used by our algorithm mimics the way a human would try to solve the same problem. Every progress made during the solving process is accompanied by a detailed…

We establish the existence of strong solutions to a class of nonlinear strongly coupled and uniform elliptic systems consisting of more than two equations. The existence of of nontrivial and non constant solutions (or pattern formations)…

The method of solving of nonlinear Schr\"odinger equation is considered. Some examples of its applications are demonstrated.

This paper is concerned with the problem of finding a quadratic common Lyapunov function for a family of stable linear systems. We present gradient iteration algorithms which give deterministic convergence for finite system families and…

We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…

We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…

A system of linear equations is normally understood as a linear mapping between two vector spaces. However, most direct solutions (e.g., QR, LU, ...) rely on the inelegant approach of back-substitution: a significant departure from such a…

We show that if the probabilistic logarithmic-space solver or the deterministic nearly logarithmic-space solver for undirected Laplacian matrices can be extended to solve slightly larger subclasses of linear systems, then they can be use to…

Line congruences are $2$-dimensional families of lines in $3$-space. The singularities that appear in generic line congruences are folds, cusps and swallowtails. In this paper we give a geometric description of these singularities. The main…

The equivalence test is a main part in any classification problem. It helps to prove bounds for the main parameters of the considered combinatorial structures and to study their properties. In this paper, we present algorithms for…

We present an algorithm for detecting basepoints of linear series of curves in the plane. Moreover, we give an algorithm for constructing a linear series of curves in the plane for given basepoints. The underlying method of these algorithms…

We develop a new tool, namely polynomial and linear algebraic methods, for studying systems of word equations. We illustrate its usefulness by giving essentially simpler proofs of several hard problems. At the same time we prove extensions…

In this study, a recursive solution technique in conjunction with generalized integrating factors is presented and applied to address first and second order linear differential equations. This approach demonstrates practical utility in…

We examine a class of geometric theorems on cyclic 2n-gons. We prove that if we take n disjoint pairs of sides, each pair separated by an even number of polygon sides, then there is a linear combination of the angles between those sides…

We generalize several recognizability theorems for free single-sorted algebras to the field of many-sorted algebras and provide, in a uniform way and without using neither regular tree grammars nor tree automata, purely algebraic proofs of…

This paper proposes a new gradient method to solve the large-scale problems. Theoretical analysis shows that the new method has finite termination property for two dimensions and converges R-linearly for any dimensions. Experimental results…

In this article we develop and analyze novel iterative regularization techniques for the solution of systems of nonlinear ill--posed operator equations. The basic idea consists in considering separately each equation of this system and…

Two essential methods, the symmetry analysis and of the singularity analysis, for the study of the integrability of nonlinear ordinary differential equations are discussed. The main similarities and differences of these two different…

Congruences for stochastic automata are defined, the correspondin factor automata are constructed and investigated for automata ove analytic spaces. We study the behavior under finite and infinite streams. Congruences consist of multiple…