1. Interval max-plus matrix equations.
- Author
-
Myšková, Helena
- Subjects
- *
NUMERICAL analysis , *MATHEMATICS , *EQUATIONS , *ALGEBRA , *HILBERT'S tenth problem - Abstract
This paper deals with the solvability of interval matrix equations in max-plus algebra. Max-plus algebra is the algebraic structure in which classical addition and multiplication are replaced by ⊕ and ⊗, where a ⊕ b = max { a , b } and a ⊗ b = a + b . The notation A ⊗ X ⊗ C = B represents an interval max-plus matrix equation, where A , B , and C are given interval matrices. We define four types of solvability of interval max-plus matrix equations, i.e., the tolerance, weak tolerance, left-weak tolerance, and right-weak tolerance solvability. We derive the necessary and sufficient conditions for checking each of them, whereby all can be verified in polynomial time. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF