Appendix 2B: Proof that the least-squares minimization of a constrained model is equal to the least-squares minimization of an unconstrained model of projected data on the space where the constraint is valid.. Appendix 1: Orthogonality between the column spaces of the matrices in equation [5] 133 6.8.2 Appendix 2: Proof that the least-squares minimization of a constrained model is equal to the ...

The diffusion tensor is typically assumed to be positive definite. However, noise in the measurements may cause the eigenvalues of the tensor estimate to be negative, thereby violating this assumption. Negative eigenvalues in diffusion tensor imaging (DTI) data occur predominately in regions of high anisotropy and may cause the fractional anisotropy (FA) to exceed unity. Two constrained least s...

This paper presents an analysis of the constrained least squares filter and a feedback structure is derived which shows the noise cancelling proper— ties of the filter, Using an identification algorithm, it is shown how the constrained least squares filter can be replaced by a f in— ite impulse response filter which can be J.nple— mented on-line. The limitations of this F.I.R. filter are discus...

In e-learning settings, the evaluation of different alternatives regarding learning paths’ proposals is nowadays crucial, due to the great attention devoted to the construction of learning objects (LO) available through Learning Management Systems (LMS). In this paper, we present a model aiming to support this evaluation process, in presence of multiple attributes and of a panel of experts invo...

In this note we study a truncated additive normalization of the Banzhaf value. We are able to show that it corresponds to the Least Square nucleolus (LS-nucleolus), which was originally introduced as the solution of a constrained optimization problem (Ruiz et al., 1996). Thus, the main result provides an explicit expression that eases the computation and contributes to the understanding of the ...

where A is symmetric positive definite (SPD), C is symmetric semi-positive definite, and B is of full rank. System of the form (1) arises in a variety of scientific and engineering applications, such as constrained optimization, least squares. We refer the reader to [1] for a more detailed list of applications and numerical solution techniques of (1). Recently, drawing on previous works: [2, 3]...

in the linear system ax = b the points x are sometimes constrained to lie in a given subspace s of column space of a. drazin inverse for any singular or nonsingular matrix, exist and is unique. in this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of drazin inverse in solving such systems is investigated. constrained linear system arise ...