Interval Linear Algebra and Computational Complexity

TL;DR

This paper explores the intersection of computational complexity and interval linear algebra, analyzing problem tractability and providing foundational insights for future research.

Contribution

It introduces core concepts of interval linear algebra and examines their computational complexity, highlighting which problems are tractable or intractable.

Findings

Many interval linear algebra problems are intractable.

Identifies subclasses of problems that are easily solvable or decidable.

Provides foundational material for further research in the field.

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.