Parametric Interval Algebraic Systems - Skalna, Iwona; SpringerLink (Online service) (Cham : Springer International Publishing : Imprint: Springer, 2018)
This self-contained book presents a framework for solving a general class of linear systems with coefficients being continuous functions of parameters varying within prescribed intervals. It also provides a comprehensive overview of the theory related to solving parametric interval linear systems and the basic properties of parametric interval matrices. In particular, it develops several new algorithms delivering sharp rigorous bounds for the solutions of such systems with full mathematical rigor. The framework employs the arithmetic of revised affine forms that enables the readers to handle dependent data. The book is intended not only for researchers interested in developing rigorous methods of numerical linear algebra, but also for engineers dealing with problems involving uncertain data. The theory discussed is also useful in various other fields of numerical analysis, in computer graphics, economics, computational geometry, computer-aided design, computer-assisted proofs, computergraphics, control theory, solving constraint satisfaction problems, and global optimization.
Introduction -- Interval arithmetic -- Alternative arithmetic -- Interval and parametric interval matrices -- Linear systems -- Methods for solving parametric interval linear systems -- Methods for computing parametric solution -- Parametric interval linear programming problem.
Keywords: Computational intelligence; System theory; Control theory; Artificial intelligence; Computational Intelligence; Systems Theory, Control; Artificial Intelligence