Skip to content
Free planNo credit card requiredStart writing
AI for Research home
AI for Research home
Dashboard
Sign inGet started

Search 250 million research papers

Read the abstract, see who wrote it and who cites it, and get the citation in APA, MLA, Chicago or Harvard.

About 3,723 papers for “Interval arithmetic”

Complex interval arithmetic

Jon Rokne, Peter Lancaster · Communications of the ACM · 1971

Complex interval arithmetic is defined using real interval arithmetic. Complex interval division is defined so as to assure smallest possible resulting intervals.

Cited by 59Open access

Interval Arithmetic Specification

Dmitri Chiriaev, G. William Walster · 1998

Compiler support for interval arithmetic requires a specification of both the syntax and semantics of the implementation. The Fortran 77 specification contained herein defines a set of extended real intervals and their internal representation for IEEE 754 compliant processors. The defined set of extended real intervals is closed with respect to arithmetic operations and interval enclosures of real functions. For mathematical details, see [16] and [19].

Cited by 0

Interval Arithmetic With

Clp Igor, Igor Mozetic, Christian Holzbaur · 2007

We describe two extensions of CLP(!), motivated by an application to modelbased diagnosis of active analog filters. The first extension addresses the problem of rounding errors in CLP(!). We represent !eals with floating-point intervals which are computed by outward rounding. The second extension increases the expressiveness of linear CLP(!). Constants in linear expressions can now be intervals, which enables reasoning with imprecise model parameters (tolerances). Bounds (sup and inf) for individual variables are computed by the linear optimization via modified Simplex. Both extensions are implemented in a CLP shell --- an adaptation of SICStus Prolog, which allows for easy and fast developments and modifications of CLP languages. 1 Introduction The motivation for this work was the idea to use CLP(!) for the simulation and diagnosis of analog circuits. First experiments [Mozeti c et al., 1991] showed that CLP(!) has some advantages over classical simulation tools (like SPICE or Micro...

Cited by 0

Interval arithmetic backpropagation

Carmen Hernández, J. Espf, Kenji Nakayama et al. · Kanazawa University Repository for Academic Resources (DSpace) (Kanazawa University) · 2005

Presents an extension of the backpropagation learning algorithm by using interval arithmetic. The proposed algorithm represents a generalization of backpropagation and contains backpropagation as a particular case. This new algorithm permits the use of training samples and targets which can be indistinct points and intervals. Among the possible applications of this algorithm, the authors report its usefulness to integrate expert's knowledge and experimental samples and also its ability to handle "don't care attributes" in a simple and natural way in comparison with backpropagation. It also adds flexibility to the codification of inputs and outputs.

Cited by 19Open access

IABP: Interval Arithmetic Backpropagation

C. A. Hernández, J.M. Espı́, Kenji Nakayama et al. · Kanazawa University Repository for Academic Resources (DSpace) (Kanazawa University) · 1993

Cited by 0Open access

Interval Arithmetic and Standardization

Wolff von Gudenberg, Jürgen · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · 2008

Interval arithmetic is arithmetic for continuous sets. Floating-point intervals are intervals of real numbers with floating-point bounds. Operations for intervals can be efficiently implemented. There is an unanimous agreement, how to define the basic operations, if we exclude division by an interval containing zero. Hence, it should be standardized. For division by zero, two options are possible, the clean exception free interval arithmetic or the containment arithmetic. They can be standardized as options. Elementary functions for intervals can be defined. In some application areas loose evaluation of functions, i.e. evaluation over an interval which is not completely contained in the function domain, is recommended, In this case, however, a discontinuity flag has to be set to inform that Brouwer's fixed point theorem is no longer applicable in that case.

Cited by 0Open access

valr: Genome Interval Arithmetic

Jay R. Hesselberth, Kent Riemondy · 2016

Read and manipulate genome intervals and signals. Provides functionality similar to command-line tool suites within R, enabling interactive analysis and visualization of genome-scale data. Riemondy et al. (2017) &lt;<a href="https://doi.org/10.12688%2Ff1000research.11997.1" target="_top">doi:10.12688/f1000research.11997.1</a>&gt;.

Cited by 0Open access

Applying Interval Arithmetic to . . .

Frederic Benhamou, William J. Older · 2008

We present in this paper a uni ed processing for Real, Integer and Boolean Constraints based on a general narrowing algorithm which applies to any n-ary relation on &amp;lt;. The basic idea is to de ne, for every such relation, a narrowing function;! based on the approximation of by a Cartesian product of intervals whose bounds are oating point numbers. We then focus on non-convex relations and establish several properties. The more important of these properties is applied to justify the computation of usual relations de ned in terms of intersections of simpler relations. We extend the scope of the narrowing algorithm used in the language BNR-Prolog to integer and disequality constraints, to Boolean constraints and to relations mixing numerical and Boolean values. As a result, we propose a new Constraint Logic Programming language called CLP(BNR), where BNR stands for Booleans, Naturals and Reals. In this language, constraints are expressed in a unique structure, allowing the mixing of real numbers, integers and Booleans. We end with the presentation of several examples showing the advantages of such an approach from the point of view of the expressiveness, and give some preliminary computational results from a prototype.

Cited by 0

Testing interval arithmetic libraries

Revol, Nathalie, Benet Fernández, Luis, Ferranti, Luca et al. · Institutional Repository of Leibniz Universität Hannover (Leibniz Universität Hannover) · 2022

[no abstract available]

Cited by 0Open access

Hard-wiring interval arithmetic

Malins, E J · OpenGrey (Institut de l'Information Scientifique et Technique) · 2008

Floating point arithmetic has become prevalent in virtually every scientific computation, yet suffers from rounding, truncation and catastrophic cancellation errors to the extent that the result may be completely inaccurate. Whilst modern processors do not have the capabilities to natively support interval arithmetic, it can be implemented in software though such a method of implementation results in larger program size and often more than doubles execution times. Embedded systems do not have the luxury of utilising software implementations of interval arithmetic and so a hardware based alternative must be sought. This thesis examines the algorithms traditionally used for interval multiplication and proposes a new method, free of the caveats which plague traditional multiplication computation. The inherent parallelism of these algorithms is examined to determine their throughput and latency characteristics, given a selection of platforms which exhibit variations in the number of input buses, FPUs and result buses. A software implementation of each method of interval multiplication is described, alongside their relative performances. Given the data-dependant nature of interval computation and the current trend towards vector processing architectures, these software implementations include reformulations of both tradi- tional methods of interval multiplication to provide vectorisation of the software and thus completely eliminate branching. Realised as co-processors to the Altera Nios Il, this thesis describes the design decisions, specification, area requirements, power utilisation and per-cycle performance of hardware implementations of the brute-force, nine case and herein presented integer-based interval multipliers.

Cited by 0Open access

Introduction to interval arithmetic

Revol, Nathalie, Institut National de Recherche en Informatique et en Automatique (INRIA), 54 - Villers-les-Nancy (France). Unite de Recherche de Lorraine · OpenGrey (Institut de l'Information Scientifique et Technique) · 2001

Cited by 0

The Interval Arithmetic Package.

J. M. Yohe · Defense Technical Information Center (DTIC) · 1977

This report provides user documentation and technical documentation for a package of FORTRAN subroutines for performing interval arithmetic calculations. Apart from a relatively small number of primitives and constants, the package is directly transferrable to most large scale computing systems, and information for implementing the package on other systems is included. The implementation described herein is that for UNIVAC 1110, but the package has also been implemented on CDC, DEC, Honeywell, and IBM equipment. (Author)

Cited by 4