Interval strong solutions of interval systems of max-plus linear equations

• Published in: Linear algebra and its applications Vol. 537; pp. 148 - 159
• Main Authors: Wang, Cailu, Tao, Yuegang
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 15.01.2018; American Elsevier Company, Inc
• Subjects: Interval arithmetic; Interval strong solution; Interval system; Linear algebra; Linear equations; Max-plus linear equations; Multiplication & division; Polynomial algorithm; Polynomials; Strong solvability; Uniqueness; Max-plus linear equations; Interval strong solution; 65G30; 15A06; Polynomial algorithm; 15A80; Strong solvability; Interval system
• ISSN: 0024-3795; 1873-1856
• DOI: 10.1016/j.laa.2017.10.001

This paper considers the existence and uniqueness of interval strong solutions of interval systems of max-plus linear equations. A necessary and sufficient condition for the existence of interval strong solutions is presented. The proof of the existence of interval strong solutions is constructive and results in a formula for computing such solutions. A necessary and sufficient condition for the uniqueness of interval strong solutions is established by testing the unique solvability of a finite number of subsystems rather than all subsystems. On this basis, a polynomial algorithm is developed to verify the uniqueness of interval strong solutions.