Journal ArticleDOI
On interval enclosures using slope arithmetic
Shen Zuhe,M. A. Wolfe +1 more
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TLDR
In this article, a combination of interval derivative arithmetic and interval slope arithmetic can be used with the programming language Pascal-SC to obtain an enclosure of the range of a factorable function with @? @? C^2 (D) which is often narrower than that which is obtained by using slope arithmetic alone and which is always narrower than the one obtained by interval derivative algebra alone.About:
This article is published in Applied Mathematics and Computation.The article was published on 1990-09-01. It has received 28 citations till now. The article focuses on the topics: Interval arithmetic.read more
Citations
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Book
Introduction to Interval Analysis
TL;DR: This unique book provides an introduction to a subject whose use has steadily increased over the past 40 years, and provides broad coverage of the subject as well as the historical perspective of one of the originators of modern interval analysis.
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A New Method for Global Solution of Systems of Non-Linear Equations
TL;DR: A new method for solving the global solution problem is suggested, based on a transformation of the original system into a larger system of separable form, which is found in a most efficient manner by a new interval method which exploits the separabily property.
Journal ArticleDOI
Automatic Computation of a Linear Interval Enclosure
TL;DR: A new algorithm for determining the coefficients ai and the interval B of F(X) is proposed based on the introduction of a specific generalized representation of intervals which permits the computation of the enclosure considered to be fully automated.
Journal ArticleDOI
An interval method for global nonlinear analysis
TL;DR: A new iterative interval method for solving the global nonlinear analysis (GNA) problem is suggested, based on the following techniques: transformation of the original system into an augmented system of n+m equations of n' variables by introducing m auxiliary variables, and solution of the resulting reduced size n/spl times/n linear system.
Journal ArticleDOI
An improved interval linearization for solving nonlinear problems
TL;DR: Numerical examples illustrating the superiority of L(x,y)=Ax+By+b over L( x)=Ax-By-b have been solved for the case where the problem is the global solution of a system of nonlinear equations (n=m).
References
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Book
Introduction to Interval Computation
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.
Book
Encyclopedia of Computer Science
TL;DR: This new edition of the Encyclopedia of Computer Science has 2,000 pages containing over 600 fully-updated articles by internationally-known computing experts, and over 100 new articles covering emerging, cutting-edge subjects.
Journal ArticleDOI
Global optimization using interval analysis -- the multi-dimensional case
TL;DR: In this paper, interval analysis is used to compute the global minimum of a function of n variables over ann-dimensional parallelopiped with sides parallel to the coordinate axes, providing infallible bounds on both the globally minimum value of the function and the point(s) at which the minimum occurs.