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Interval Systems of Linear Equations

In: Interval Linear Programming and Extensions

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  • Milan Hladík

    (Charles University)

Abstract

Solving systems of linear equations is a basic problem in linear algebra, but it is also essential for many other disciplines, including optimization. Not surprisingly, problems related to interval linear equations are fundamental in interval computation and interval linear programming. In interval problems, there is no natural definition of a solution. So, we begin with an introduction to the quite usual concept of (weak) solutions that the chapter is devoted to. We present the characterization of the solution set, its geometry (nonconvex polyhedra), and its computational complexity (NP-hard). To solve interval linear equations, we discuss several enclosure (both direct and iterative) methods and also some exact methods. As a related problem, we address the regularity of interval matrices.

Suggested Citation

  • Milan Hladík, 2025. "Interval Systems of Linear Equations," Springer Optimization and Its Applications, in: Interval Linear Programming and Extensions, chapter 0, pages 45-74, Springer.
    • Handle: RePEc:spr:spochp:978-3-031-85096-7_3
    DOI: 10.1007/978-3-031-85096-7_3
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