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Interval Mathematics 1980
- 1st Edition - May 10, 2014
- Editor: Karl L. E. Nickel
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 4 4 1 3 - 6
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 7 3 8 4 - 6
Interval Mathematics 1980 contains the proceedings of an International Symposium on Interval Mathematics held in Germany on May 27-31, 1980. The book introduces the reader to some… Read more
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Request a sales quoteInterval Mathematics 1980 contains the proceedings of an International Symposium on Interval Mathematics held in Germany on May 27-31, 1980. The book introduces the reader to some of the most important work done in the field of interval mathematics and its application to computing. Topics covered range from purely theoretical to computational methods and computer architecture. Comprised of 41 chapters, this book begins with an overview of set functions and their applications, followed by a discussion on global constrained optimization using interval analysis. A model for the propagation of rounding error in floating arithmetic is then presented, and the importance of 3-valued notions for interval mathematics is highlighted. Subsequent chapters focus on the transformation of interval programs into convergent interval programs; specifications for interval programming languages; interval contractions for the solution of integral equations; and mean convergence enclosing of solutions of operator equations with convex and inverse monotonic operators. This monograph will be of value to both students and specialists in the fields of mathematics and computer science.
Contributors
Foreword
Preface
Invited Lectures
Set Functions and Applications
Global Constrained Optimization Using Interval Analysis
A Model for the Propagation of Rounding Error in Floating Arithmetic
The Importance of 3-Valued Notions for Interval Mathematics
Interval Arithmetic Options in the Proposed IEEE Floating Point Arithmetic Standard
Interval Components of Non-Archimedean Number Systems
Interval Differential Equations
New Results on Nonlinear Systems
Optimal Approximations in Interval Analysis
Some Topics of Segment Analysis
Rounding Error in Gaussian Elimination of Tridiagonal Linear Systems. Survey of Results
Contributed Lectures
On Sets of Solutions of Collections of Nonlinear Systems in IRn
About the Transformation of Interval Programs into Convergent Interval Programs
Specifications for Interval Programming Languages
Interval Contractions for the Solution of Integral Equations
Rounding Invariant Structures by Application of a Mapping of a Ringoid in an Ordered Set
SIGLA-PL/1. Development and Applications
Totally Nonnegative Interval Matrices
Using Scalar and Vector Majorizing Equations to Bound Solution Sets of Nonlinear Algebraic Equation Systems
Application of Interval Analysis to Linear Problems of Optimal Control with Quadratic Cost Functional
Interpolation of Interval-Valued Functions with Restrictions
A Programming System for Interval Arithmetic in ALGOL 68
Extended Circular Arithmetic, Problems and Results
Locating Safe Starting Regions for Iterative Methods: A Heuristic Algorithm
Comparison of Diverse Iteration Methods for Sets
On Discrete Equations, Inequalities, and Interval Evaluations of Fixed Points of Isotone-Antitone Mappings
Evaluation of Complex Logarithms and Related Functions with Interval Arithmetic
Linear Transformations of Vector Sets and Their Applications
Bounding Eigenvectors of a Symmetric Matrix
Computing the Exponential of an Essentially Nonnegative Matrix
Convergent-Optimal Roundings in Totally Ordered Sets
On the Generalization of Some Algorithms for the Simultaneous Approximation of Polynomial Roots
On a Representation of the k-th Root in Complex Circular Interval Arithmetic
A Generalization of the Krawczyk-Moore Algorithm
Optimization of Interval Computation
Optimality of the Centered Form
Interval Power Series
Duality in Interval Linear Programming
Mean Convergence Enclosing of Solutions of Operator Equations with Convex and Inverse Monotonic Operators
Domains with all Solutions of Nonlinear Problems with Non-Inverse-Isotonic Operators
Floating Point Exception Handling for Interval Arithmetic
- No. of pages: 570
- Language: English
- Edition: 1
- Published: May 10, 2014
- Imprint: Academic Press
- Paperback ISBN: 9781483244136
- eBook ISBN: 9781483273846
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