Parametric Interval Algebraic Systems

Nonfiction, Science & Nature, Science, Other Sciences, System Theory, Computers, Advanced Computing, Artificial Intelligence, General Computing
Cover of the book Parametric Interval Algebraic Systems by Iwona Skalna, Springer International Publishing
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Author: Iwona Skalna ISBN: 9783319751870
Publisher: Springer International Publishing Publication: February 9, 2018
Imprint: Springer Language: English
Author: Iwona Skalna
ISBN: 9783319751870
Publisher: Springer International Publishing
Publication: February 9, 2018
Imprint: Springer
Language: English

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, computer graphics, control theory, solving constraint satisfaction problems, and global optimization.

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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, computer graphics, control theory, solving constraint satisfaction problems, and global optimization.

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