Interval Linear Algebra and Computational Complexity

Abstract

This work connects two mathematical fields – computational complexity and interval linear algebra . It introduces the basic topics of interval linear algebra – regularity and singularity, full column rank, solving a linear system , deciding solvability of a linear system , computing inverse matrix , eigenvalues , checking positive (semi)definiteness or stability . We discuss these problems and relations between them from the view of computational complexity . Many problems in interval linear algebra are intractable, hence we emphasize subclasses of these problems that are easily solvable or decidable. The aim of this work is to provide a basic insight into this field and to provide materials for further reading and research.