Determining the solution of some overdetermined systems of equations Ax = b, A ∈ Rm×n, x ∈ Rn and b ∈ Rm, may not be a well-posed problem. Specifically, this means that in some cases small changes in the right hand side vector b can lead to relatively larger changes in the solution vector x. Problems for which this occurs are called ill-posed. For example the deblurring of an image or the resto...

ABSTRACT We compare a particular selection of approximate solutions the Riemann problem in context ideal relativistic magnetohydrodynamics. In particular, we focus on solvers not requiring full eigenvector structure. Such recover solution by solving simplified or reduced set jump conditions, whose level complexity depends intermediate modes that are included. Five different approaches – namely ...

One previous paradigm was based on sensor positioning selection to allow key variable observability. Later, the problem was posed as a minimum cost problem subject to sensor network performance (precision and gross error robustness first and accuracy as a replacement later). In a previous paper (Nguyen ccepted 12 July 2010 vailable online 18 July 2010

satisfying the prescribed final-value, u(T) = f. We assume A is maximal accretive, so the problem is generally not well-posed. Assume in addition that A2 is accretive. We shall demonstrate that there is at most one solution of this problem, and we give a constructive quasireversibility method of constructing solutions of (1.1) which approximately satisfy the final condition. In particular, one ...

The goal of this paper is to provide an overview of results concerning, roughly speaking, the following issue: given a (topologized) class of minimum problems, “how many” of them are well-posed? We will consider several ways to define the concept of “how many,” and also several types of well-posedness concepts. We will concentrate our attention on results related to uniform convergence on bound...

The present paper establishes a certain duality between the Dirichlet and Regularity problems for elliptic operators with t-independent complex bounded measurable coefficients (t being the transversal direction to the boundary). To be precise, we show that the Dirichlet boundary value problem is solvable in Lp ′ , subject to the square function and non-tangential maximal function estimates, if ...

In this paper, we consider the second-kind Chebyshev polynomials (SKCPs) for the numerical solution of the fractional optimal control problems (FOCPs). Firstly, an introduction of the fractional calculus and properties of the shifted SKCPs are given and then operational matrix of fractional integration is introduced. Next, these properties are used together with the Legendre-Gauss quadrature fo...

We consider the problem of determining the conductivity in a heat equation from overspecified non-smooth data. It is an ill-posed inverse problem. We apply a regularization approach to define and construct a stable approximate solution. We also conduct numerical simulation to demonstrate the accuracy of our approximation.

lack of fire behavior studies and the immediate needs posed by the extent of the fire problem in forests of iran require that extensive studies be conducted to develop models to predict fire behavior in the region.in this study, farsite fire area simulator was applied to simulate spread and behavior of two real fires that had occurred in northern forests of iran during 2010 summer and fall seas...