Topic
Interval (mathematics)
About: Interval (mathematics) is a research topic. Over the lifetime, 11686 publications have been published within this topic receiving 179954 citations. The topic is also known as: real interval.
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Journal Article•
TL;DR: An interval-based temporal logic is introduced, together with a computationally effective reasoning algorithm based on constraint propagation, which is notable in offering a delicate balance between space and time.
Abstract: An interval-based temporal logic is introduced, together with a computationally effective reasoning algorithm based on constraint propagation. This system is notable in offering a delicate balance between
7,466 citations
Book•
02 Jan 2016
TL;DR: In this paper, the authors present an ALGOLGOL-based approach for the inclusion of complex Zeros of polynomials of a function of one real variable in a system of linear systems of equations.
Abstract: Preface to the English Edition. Preface to the German Edition. Real Interval Arithmetic. Further Concepts and Properties. Interval Evaluation and Range of Real Functions. Machine Interval Arithmetic. Complex Interval Arithmetic. Metric, Absolute, Value, and Width in. Inclusion of Zeros of a Function of One Real Variable. Methods for the Simultaneous Inclusion of Real Zeros of Polynomials. Methods for the Simultaneous Inclusion of Complex Zeros of Polynomials. Interval Matrix Operations. Fixed Point Iteration for Nonlinear Systems of Equations. Systems of Linear Equations Amenable to Interation. Optimality of the Symmetric Single Step Method with Taking Intersection after Every Component. On the Feasibility of the Gaussian Algorithm for Systems of Equations with Intervals as Coefficients. Hansen's Method. The Procedure of Kupermann and Hansen. Ireation Methods for the Inclusion of the Inverse Matrix and for Triangular Decompositions. Newton-like Methods for Nonlinear Systems of Equations. Newton-like Methods without Matrix Inversions. Newton-like Methods for Particular Systems of Nonlinear Equations. Newton-like Total step and Single Step Methods. Appendix A. The Order of Convergence of Iteration Methods in vn(Ic) and Mmn(iC) ). Appendix B. Realizations of Machine Interval Arithmetics in ALGOL 60. Appendix C. ALGOL Procedures. Bibliography. Index of Notation. Subject Index.
2,054 citations
TL;DR: It is shown that the STP, which subsumes the major part of Vilain and Kautz's point algebra, can be solved in polynomial time and the applicability of path consistency algorithms as preprocessing of temporal problems is studied, to demonstrate their termination and bound their complexities.
1,989 citations
TL;DR: An efficient and simplified method to compute the input and antecedent operations for interval type-2 FLSs: one that is based on a general inference formula for them is proposed.
Abstract: We present the theory and design of interval type-2 fuzzy logic systems (FLSs). We propose an efficient and simplified method to compute the input and antecedent operations for interval type-2 FLSs: one that is based on a general inference formula for them. We introduce the concept of upper and lower membership functions (MFs) and illustrate our efficient inference method for the case of Gaussian primary MFs. We also propose a method for designing an interval type-2 FLS in which we tune its parameters. Finally, we design type-2 FLSs to perform time-series forecasting when a nonstationary time-series is corrupted by additive noise where SNR is uncertain and demonstrate an improved performance over type-1 FLSs.
1,845 citations
TL;DR: This Second Edition of Global Optimization Using Interval Analysis expands and improves various aspects of its forerunner and features significant new discussions, such as those on the use of consistency methods to enhance algorithm performance.
Abstract: Employing a closed set-theoretic foundation for interval computations, Global Optimization Using Interval Analysis simplifies algorithm construction and increases generality of interval arithmetic. This Second Edition contains an up-to-date discussion of interval methods for solving systems of nonlinear equations and global optimization problems. It expands and improves various aspects of its forerunner and features significant new discussions, such as those on the use of consistency methods to enhance algorithm performance. Provided algorithms are guaranteed to find and bound all solutions to these problems despite bounded errors in data, in approximations, and from use of rounded arithmetic.
1,705 citations