Prior knowledge over general nonlinear sets is incorporated into nonlinear kernel proximal classification problems as linear equalities. The key tool in this incorporation is the conversion of general nonlinear prior knowledge implications into linear equalities in the classification variables without the need to kernelize these implications. These equalities are then included into a proximal n...

A method for calculating the strict Chebyshev solution of overdetermined systems of linear equations using linear programming techniques is described. This method provides: (1) a way to determine, for the majority of cases, all the equations belonging to the characteristic set, (2) an efficient method to obtain the inverse of the matrix needed to calculate the strict Chebyshev solution, and (3)...

We consider a system of m linear equations in n variables Ax = d and give necessary and sufficient conditions for the existence of a unique solution to the system that is integer: x ∈ {−1,1}n. We achieve this by reformulating the problem as a linear program and deriving necessary and sufficient conditions for the integer solution to be the unique primal optimal solution. We show that as long as...

This paper studies the identification problem in infinite horizon Markovian games and proposes a generally applicable estimation method. Every period firms simultaneously select an action from a finite set. We characterize the set of Markov equilibria. Period profits are a linear function of equilibrium choice probabilities. The question of identification of these values is then reduced to the ...

We address in this paper the following two closely related problems: 1. How to represent functions with singularities (up to a prescribed accuracy) in a compact way? 2. How to reconstruct such functions from a small number of measurements? The stress is on a comparison of linear and nonlinear approaches. As a model case we use piecewise-constant functions on [0, 1], in particular, the Heaviside...

Effective matrix methods for solving standard linear algebra problems in a commutative domains are discussed. Two of them are new. There are a methods for computing adjoined matrices and solving system of linear equations in a commutative domains.

Discretization of non-linear Poisson-Boltzmann Equation equations results in a system of non-linear equations with symmetric Jacobian. The Newton algorithm is the most useful tool for solving non-linear equations. It consists of solving a series of linear system of equations (Jacobian system). In this article, we adaptively define the tolerance of the Jacobian systems. Numerical experiment show...

We obtain linearized oscillation theorems for the equation with distributed delays ẋ(t)+ m ∑ k=1 rk(t) ∫ t −∞ fk(x(s)) ds Rk(t, s) = 0. (1) The results are applied to logistic, Lasota–Wazewska and Nicholson’s blowflies equations with a distributed delay. In addition, the “Mean Value Theorem” is proved which claims that a solution of (1) also satisfies the linear equation with a variable concent...

in this paper, an iterative method is proposed for solving large general sylvester matrix equation $axb+cxd = e$, where $a in r^{ntimes n}$ , $c in r^{ntimes n}$ , $b in r^{stimes s}$ and  $d in r^{stimes s}$ are given matrices and $x in r^{stimes s}$  is the unknown matrix. we present a global conjugate gradient (gl-cg) algo- rithm for solving linear system of equations with multiple right-han...