Exact real arithmetic for interval number systems

被引：4
|
作者：
Kurka, Petr [1 ,2 ]
机构：
[1] Acad Sci Czech Republic, Ctr Theoret Study, CZ-11000 Prague 1, Czech Republic
[2] Charles Univ Prague, CZ-11000 Prague 1, Czech Republic
来源：
THEORETICAL COMPUTER SCIENCE | 2014年 / 542卷
关键词：
Mobius transformation; Exact real arithmetic;
D O I：
10.1016/j.tcs.2014.04.030
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
An interval number system is given by an initial interval cover of the extended real line and by a finite system of nonnegative Mobius transformations. Each sequence of transformations applied to an initial interval determines a sequence of nested intervals whose intersection contains a unique real number. We adapt in this setting the exact real algorithms which compute arithmetical operations to arbitrary precision. (C) 2014 Elsevier B.V. All rights reserved.
引用
收藏
页码：32 / 43
页数：12
相关论文
共 50 条
  • [41] ARITHMETIC CODES IN RESIDUE NUMBER-SYSTEMS
    BARSI, F
    MAESTRINI, P
    DIGITAL PROCESSES, 1978, 4 (02): : 121 - 135
  • [42] KLOSE,OM - NUMBER SYSTEMS AND OPERATIONS OF ARITHMETIC
    GRUBER, P
    MONATSHEFTE FUR MATHEMATIK, 1967, 71 (02): : 180 - &
  • [43] ON STABILIZATION OF SYSTEMS WITH UNCERTAIN PARAMETERS - AN INTERVAL ARITHMETIC APPROACH
    MISRA, P
    PROCEEDINGS OF THE 1989 AMERICAN CONTROL CONFERENCE, VOLS 1-3, 1989, : 657 - 658
  • [44] Certifying Zeros of Polynomial Systems Using Interval Arithmetic
    Breiding, Paul
    Rose, Kemal
    Timme, Sascha
    ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 2023, 49 (01):
  • [45] INTERVAL ARITHMETIC APPROACH TO QUALITATIVE PHYSICS - STATIC SYSTEMS
    CHANG, IC
    YU, CC
    LIOU, CT
    INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 1993, 8 (03) : 405 - 430
  • [46] On the selection of a transversal to solve nonlinear systems with interval arithmetic
    Goualard, Frederic
    Jermann, Christophe
    COMPUTATIONAL SCIENCE - ICCS 2006, PT 1, PROCEEDINGS, 2006, 3991 : 332 - 339
  • [47] EXACT COVERING SYSTEMS IN NUMBER FIELDS
    Jiang, Yupeng
    Deng, Yingpu
    QUARTERLY JOURNAL OF MATHEMATICS, 2014, 65 (01): : 211 - 223
  • [48] RMPC for constrained nonlinear systems based on interval arithmetic
    Qin, W.-W. (qww_1982@163.com), 1600, South China University of Technology (31):
  • [49] Applications of interval arithmetic to the analysis and control of structural systems
    Del Grosso, A.
    Zucchini, A.
    Smart Materials and Structures, 1993, 2 (02) : 103 - 112
  • [50] Solving nonlinear systems by constraint inversion and interval arithmetic
    Ceberio, M
    Granvilliers, L
    ARTIFICIAL INTELLIGENCE AND SYMBOLIC COMPUTATION, 2001, 1930 : 127 - 141
12345