On rank range of interval matrices

An interval matrix is a matrix whose entries are intervals in the set of real numbers. Let $p , q$ be nonzero natural numbers and let $\mu =( [m_{i,j}, M_{i,j}])_{i,j}$ be a $p \times q$ interval matrix; given a $p \times q$ matrix $A$ with entries in the set of real numbers, we say that $A \in \mu$ if $a_{i,j} \in [m_{i,j}, M_{i,j}]$ for any $i,j$. We establish a criterion to say if an interval matrix contains a matrix of rank $1$. Moreover we determine the maximum rank of the matrices contained in a given interval matrix. Finally, for any interval matrix $\mu$ with no more than $3$ columns, we describe a way to find the range of the ranks of the matrices contained in $\mu$.Comment: corrected Section

Computing Enclosures of Overdetermined Interval Linear Systems

This work considers special types of interval linear systems - overdetermined systems. Simply said these systems have 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 interval system. Enclosing the solution set of these systems is in some ways more difficult than for square systems. The main goal of this work is to present various methods for solving overdetermined interval linear systems. We would like to present them in an understandable way even for nonspecialists in a field of linear systems. The second goal is a numerical comparison of all the methods on random interval linear systems regarding widths of enclosures, computation times and other special properties of methods.Comment: Presented at SCAN 201

Enclosing solutions of overdetermined systems of linear interval equations

A method for enclosing solutions of overdetermined systems of linear interval equations is described. Several aspects of the problem (algorithm, enclosure improvement, optimal enclosure) are studied.