We propose the use of the preconditioned interval Gauss-Seidel method as the backbone of an eecient linear equality solver in a CLP(Interval) language. The method, as originally designed, works only on linear systems with square coeecient matrices. Even imposing such a restriction, a naive incorporation of the traditional precon-ditioning algorithm in a CLP language incurs a high worst-case tim...

In this paper, the problem of delay dependent robust asymptotically stable for uncertain linear time-variant system with multiple delays is investigated. A new delay-dependent stability sufficient condition is given by using the Lyapunov method, linear matrix inequality (LMI), parameterized first-order model transformation technique and transformation of the interval uncertainty in to the norm ...

The purpose of this paper is to inquire the connection between maximal inner interval estimates of the solution sets to interval linear system and solutions of the dualization equation in Kaucher interval arithmetic. The results of our work are as follows: 1) a criterion of inner interval estimate of the solution set, 2) a criterion for a solution of dualization equation to be a maximal inner i...

Many mechanical systems, involving interval uncertainties and modelled by finite element method, can be described by parameter dependent systems of linear interval equations and response quantities depending on the system solution. A newly developed hybrid interval approach for solving parametric interval linear systems is applied to a 2D engineering model with interval parameters and the resul...

Partially identified models occur commonly in economic applications. A common problem in this literature is a regression problem with bracketed (interval-censored) outcome variable Y , which creates a set-identified parameter of interest. The recent studies have only considered finitedimensional linear regression in such context. To incorporate more complex controls into the problem, we conside...

Generalized intervals (intervals whose bounds are not constrained to be increasingly ordered) extend classical intervals providing better algebraic properties. In particular, the generalized interval arithmetic is a group for addition and for multiplication of zero free intervals. These properties allow one constructing a LU decomposition of a generalized interval matrix A: the two computed gen...

Fuzzy data given by expert knowledge can be regarded as a possibility distribution by which possibilistic linear systems are defined. Recently, it has become important to deal with fuzzy data in connection with expert knowledge. Three formulations of possibilistic linear regression analysis are proposed here to deal with fuzzy data. Since our formulations can be reduced to linear programming pr...

This work considers special types of interval linear systems overdetermined systems, systems consisting of more equations than variables. The solution set of an interval linear system is a collection of all solutions of all instances of an interval system. By the instance, we mean a point real system that emerges when we independently choose a real number from each interval coefficient of the i...