It is a fundamental fact about simultaneous linear equations that uniqueness implies existence in the sense that if the »X» system MX= Y has, for each Y, at most one solution X, then, for each Y, the equation actually has a solution. Our purpose is to show that this situation persists for certain "nonlinear equations" as well, namely that, restricting everything to the reals, if Pi, P2 are poly...

in this paper, an effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (rbfs). we present an algorithm based on interpolation by radial basis functions including multiquadratics (mqs), using legendre-gauss-lobatto nodes and weights. also a theorem is proved for convergence of the algorithm. some numerical examples are presented...

Simultaneous Embedding with Fixed Edges (SEFE) [1] is a problem where given k planar graphs we ask whether they can be simultaneously embedded so that the embedding of each graph is planar and common edges are drawn the same. Problems of SEFE type have inspired questions of Simultaneous Geometrical Representations and further derivations. Based on this motivation we investigate the generalizati...

Parametric design is very stable but requires a predefined dimensioning and ordering scheme, thus limiting flexibility and precluding sketch input. Variational geometry design, while general and flexible, necessitates intensive use of numerical solvers to solve many simultaneous nonlinear equations. Frequently the solvers cannot solve these equations. A new system, based on an original theory f...

We study the simultaneous blow-up rates of a system of two heat equations coupled through the boundary in a nonlinear way. We complete the previous known results by covering the whole range of possible parameters.

We study two-dimensional triangular systems of Newton equations (acceleration = velocity-independent force) admitting three functionally independent quadratic integrals of motion. The main idea is to exploit the fact that the first component M1(q1) of a triangular force depends on one variable only. By using the existence of extra integrals of motion we reduce the problem to solving a simultane...

in this paper, we will compare a homotopy perturbation algorithm and taylor series expansin method for a system of second kind fredholm integral equations. an application of he’s homotopy perturbation method is applied to solve the system of fredholm integral equations. taylor series expansin method reduce the system of integral equations to a linear system of ordinary differential equation.

A generalized maximum entropy estimator is developed for the linear simultaneous equations model. Monte Carlo sampling experiments are used to evaluate the estimator’s performance in small and medium sized samples, suggesting contexts in which the current generalized maximum entropy estimator is superior in mean square error to two and three stage least squares. Analytical results are provided ...

In practice structural equations are often estimated by least-squares, thus neglecting any simultaneity. This paper reveals why this may often be justi…able and when. Assuming data stationarity and existence of the …rst four moments of the disturbances we …nd the limiting distribution of the ordinary least-squares (OLS) estimator in a linear simultaneous equations model. In simple static and dy...