In this section, we compare the performance of minimizing the TU relaxation g∗∗ G,G of the proposed Sparse G-group cover (c.f., Section 5.4) in problem (2), which we will call Sparse latent group lasso (SLGL), with Basis pursuit (BP) and Sparse group Lasso (SGL). Recall the SGL criteria is (1 − α) ∑ G∈G √ |G|‖xG‖q + α‖xG‖1, with q = 2 in [3]. We compare also against SGL∞ where we set q = ∞, whi...

By using a new set of arithmetic operations on interval numbers, we discuss some arithmetic properties of interval matrices which intern helps us to compute the powers of interval matrices and to solve the system of interval linear equations. Keywords—Interval arithmetic, Interval matrix, linear equations.

A right-preconditioning process for linear interval systems has been presented by Neumaier in 1987. It allows the construction of an outer estimate of the united solution set of a square linear interval system in the form of a parallelepiped. The denomination ”right-preconditioning” is used to describe the preconditioning processes which involve the matrix product AC in contrast to the (usual) ...

the matrix functions appear in several applications in engineering and sciences. the computation of these functions almost involved complicated theory. thus, improving the concept theoretically seems unavoidable to obtain some new relations and algorithms for evaluating these functions. the aim of this paper is proposing some new reciprocal for the function of block anti diagonal matrices. more...

We consider the linear complementarity problem with uncertain data modeled by intervals, representing range of possible values. Many properties (such as solvability, uniqueness, convexity, finite number solutions etc.) are reflected constraint matrix. In order that has desired even in environment, we have to be able check them for all realizations interval data. This leads us robust matrices. p...

Context. The pairwise comparison method is a component of several decision support methodologies such as the analytic hierarchy and network processes (AHP, ANP), PROMETHEE, TOPSIS other. This results in weight vector elements decision-making model based on inversely symmetrical matrices. evaluation carried out mainly by experts under conditions uncertainty. Therefore, modifications this have be...

Interval iteration can be used, in conjunction with other techniques, for rigorously bounding all solutions to a nonlinear system of equations within a given region, or for verifying approximate solutions. However, because of overestimation which occurs when the interval Jacobian matrix is accumulated and applied, straightforward linearization of the original nonlinear system sometimes leads to...