Parametric Interval Algebraic Systems

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.

Provides a comprehensive overview of the theory related to the problem of solving parametric interval linear systems and investigates the basic properties of parametric interval matrices Presents a framework for solving a general class of linear systems with coefficients being continuous functions of parameters varying within prescribed intervals Includes new algorithms delivering sharp rigorous bounds for the solutions of such systems

Inhalt
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.