The least-squares method can be used to approximate an eigenvector for a matrix when only an approximation is known for the corresponding eigenvalue. In this paper, this technique is analyzed and error estimates are established proving that if the error in the eigenvalue is sufficiently small, then the error in the approximate eigenvector produced by the least-squares method is also small. Also...

| We present simple exponential approximations to the transient behavior of the stable M=M=1 queue. The approximations are optimal in a least-squares sense, and we nd them to agree well with exact results. Our approach can be used to derive approximations for any time-dependent quantity with a known Laplace transform, e.g., the probability distribution and the moments of the queue size, of the ...

The consistency and asymptotic normality of a linear least squares estimate of the form (X,X)-X’Y when the mean is not X/I is investigated in this paper. The least squares estimate is a consistent estimate of the best linear approximation of the true mean function for the design chosen. The asymptotic normality of the least squares estimate depends on the design and the asymptotic mean may not ...

Abstract In a Bayesian framework, the Dirichlet distribution is the conjugate distribution to the multinomial likelihood function, and so the analyst is required to develop a Dirichlet prior that incorporates available information. However, as it is a multiparameter distribution, choosing the Dirichlet parameters is less straightforward than choosing a prior distribution for a single parameter,...

Abstract. This paper focuses on total least squares (TLS) problems AX ≈ B with multiple right-hand sides. Existence and uniqueness of a TLS solution for such problems was analyzed in the paper [I. Hnětynková, M. Plešinger, D. M. Sima, Z. Strakoš, and S. Van Huffel (2011)]. For TLS problems with single right-hand sides the paper [C. C. Paige and Z. Strakoš (2006)] showed how a necessary and suff...

Abstrucf-Developments in the theory of linear least-squares estimation in the last thirty years or so are outlined. Particular attention is paid to early mathematical. wurk in the field and to more modem developments showing some of the many connections between least-squares filtering and other fields.

In a recent paper of the author [A. Sidi, A new approach to vector-valued rational interpolation, J. Approx. Theory 130 (2004) 177–187], three new interpolation procedures for vector-valued functions F(z), where F : C → CN , were proposed, and some of their algebraic properties were studied. One of these procedures, denoted IMPE, was defined via the solution of a linear least-squares problem. I...

Different designs of experiments are compared according to the shape, concentration, etc. of the densities of the least-squares estimator (conditional densities, marginal densities). In contrast with D'Argenio (J. Pharmacokinetics Biopharmaceutics 9(16) (1981) 739-756), where marginal densities have been obtained by simulations, we present here a faster procedure based on well-elaborated approx...

We consider the problem of fitting linearly parameterized models, that arises in many computer vision problems such as road scene analysis. Data extracted from images usually contain non-Gaussian noise and outliers, which makes non-robust estimation methods ineffective. In this paper, we propose an overview of a Lagrangian formulation of the Half-Quadratic approach by, first, revisiting the der...

We propose a sequential method to estimate monotone convex function that consists of: (i) monotone regression via solving a constrained least square problem and (ii) convexification of the monotone regression estimate via solving an associated constrained uniform approximation problem. We show that this method is faster than the constrained least squares (LS) method. The ratio of computation ti...