Related papers: Solution Theory for Systems of Bilinear Equations
In this paper, we introduce and analyze a normalization method for solving a system of linear equations over tropical semirings. We use a normalization method to construct an associated normalized matrix, which gives a technique for solving…
A bilinear formulation for the supersymmetric two-boson equation is derived. As applications, some solutions are calculated for it. We also construct a bilinear Backlund transformation.
The paper concerns the solvability by quadratures of linear differential systems, which is one of the questions of differential Galois theory. We consider systems with regular singular points as well as those with (non-resonant) irregular…
The fundamental elements of evidential reasoning problems are described, followed by a discussion of the structure of various types of problems. Bayesian inference networks and state space formalism are used as the tool for problem…
Multidimensional systems are becoming increasingly important as they provide a promising tool for estimation, simulation and control, while going beyond the traditional setting of one-dimensional systems. The analysis of multidimensional…
We consider scalar equilibrium problems governed by a bifunction in a finite-dimensional framework. By using classical arguments in Convex Analysis, we show that under suitable generalized convexity assumptions imposed on the bifunction,…
We give necessary and sufficient existence criteria, and methods for finding, continuous solutions of linear equations whose coefficients are polynomials.
A system of singular integral equations with monotone and concave nonlinearity in the subcritical case is investigated. The specified system and its scalar analog have direct applications in various areas of physics and biology. In…
In this paper we analyze the existence of large positive radial solutions to some quasilinear elliptic systems. Also, a non-radially symmetric solution is obtained by using a lower and upper solution method. The equations are coupled by…
Matrices can be augmented by adding additional columns such that a partitioning of the matrix in blocks of rows defines mutually orthogonal subspaces. This augmented system can then be solved efficiently by a sum of projections onto these…
Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…
We give a complete complexity classification for the problem of finding a solution to a given system of equations over a fixed finite monoid, given that a solution over a more restricted monoid exists. As a corollary, we obtain a complexity…
A symbolic computational algorithm which detects " linear "` solutions of nonlinear polynomial differential equations of single functions, is developed throughout this paper.
Multi-homogeneous polynomial systems arise in many applications. We provide bit complexity estimates for solving them which, up to a few extra other factors, are quadratic in the number of solutions and linear in the height of the input…
The analysis of many physical phenomena can be reduced to the study of solutions of differential equations with polynomial coefficients. In the present work, we establish the necessary and sufficient conditions for the existence of…
We propose a method for transformating linear and nonlinear hypersingular integral equations into ordinary differential equations. Linear and nonlinear polyhypersingular integral equations are transformed into partial differential…
We find a formula for the number of solutions of linear congruence systems, by using elementary methods.
This article generalizes a recently introduced procedure to solve nonlinear systems of equations, radically departing from the conventional Newton-Raphson scheme. The original nonlinear system is first unfolded into three simpler…
To compute solutions of sparse polynomial systems efficiently we have to exploit the structure of their Newton polytopes. While the application of polyhedral methods naturally excludes solutions with zero components, an irreducible…
Reducing the conditions under which a given set satisfies the stipulations of the subset sum proposition to a set of linear relationships, the question of whether a set satisfies subset sum may be answered in a polynomial number of steps by…