The div least-squares methods have been studied by many researchers for the secondorder elliptic equations, elasticity, and the Stokes equations, and optimal error estimates have been obtained in the H(div) × H1 norm. However, there is no known convergence rate when the given data f belongs only to L2 space. In this paper, we will establish an optimal error estimate in the L2 × H1 norm with the...

Given nite subset J IR n , and a point 2 IR n , we study in this paper the possible convergence, as h ! 0, of the coeecients in least-squares approximation to f(+hh) from the space spanned by (f(+ hj) j2J. We invoke thèleast solution of the polynomial interpolation problem' to show that the coeecient do converge for a generic J and , provided that the underlying function f is suuciently smooth....

Motivated by telecommunication applications, we investigate ways to estimate the parameters of a nonhomogeneous Poisson process with linear rate over a finite interval, based on the number of counts in measurement subintervals. Such a linear arrival-rate function can serve as a component of a piecewise-linear approximation to a general arrival-rate function. We consider ordinary least squares (...

The three-loop contribution to the M S single-Higgs-doublet standard-model cross-section σ(W + L W − L → ZLZL) at s = (5MH) 2 is estimated via least-squares matching of the asymptotic Padé-approximant prediction of the next order term, a procedure that has been previously applied to QCD corrections to correlation functions and decay amplitudes. In contrast to these prior applications, the expan...

The three-loop contribution to the M S single-Higgs-doublet standard-model cross-section σ(W + L W − L → ZLZL) at s = (5MH) 2 is estimated via least-squares matching of the asymptotic Padé-approximant prediction of the next order term, a procedure that has been previously applied to QCD corrections to correlation functions and decay amplitudes. In contrast to these prior applications, the expan...

By combining the well known moving least squares approximation method and the theory of approximate approximations due to Maz’ya and Schmidt we are able to present an approximate moving least squares method which inherits the simplicity of Shepard’s method along with the accuracy of higher-order moving least squares approximations. In this paper we focus our interest on practical implementation...

In this paper, we consider an issue of great interest to all students: fairness in grading. Specifically, we represent each grade as a student’s intrinsic (overall) aptitude minus a correction representing the course’s inherent difficulty plus a statistical error. We consider two statistical methods for assigning an aptitude to each student and, simultaneously, a measure of difficulty to each c...

In this paper a modi"ed version of the standard least-squares algorithm is presented. The aim is to use the proposed modi"ed LS algorithm in linear time-varying systems. The proposed modi"cation involves the addition of extra terms to both the parameter estimates' and the covariance's update laws. We establish a series of properties on the identi"cation error, the parameter estimates and the co...

A general framework for the least squares approximation of symmetric de nite pencils subject to generalized eigenvalues constraints is developed in this paper This approach can be adapted to di erent applications including the inverse eigenvalue problem The idea is based on the observation that a natural parameterization for the set of symmetric de nite pencils with the same generalized eigenva...

where L = (Lij)m×n is a block m×n matrix differential operator of at most first order, B = (Bij)l×n is a block l × n matrix operator, U = (Ui)n×1 is unknown, F = (Fi)m×1 is a given block vector-valued function defined in Ω, G = (Gi)l×1 is a given block vector-valued function defined on ∂Ω. Assume that first-order system (1.1) has a unique solution U . Boundary conditions in a least-squares form...