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Journal articles on the topic 'Interval computing'

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Published: 5 June 2025

Last updated: 15 July 2025

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1

Kleitman, Daniel J., and Rakesh V. Vohra. "Computing the Bandwidth of Interval Graphs." SIAM Journal on Discrete Mathematics 3, no. 3 (1990): 373–75. http://dx.doi.org/10.1137/0403033.

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2

Galbraith, Steven D., John M. Pollard, and Raminder S. Ruprai. "Computing discrete logarithms in an interval." Mathematics of Computation 82, no. 282 (2012): 1181–95. http://dx.doi.org/10.1090/s0025-5718-2012-02641-x.

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3

Kim, Minkyu, and Jung Hee Cheon. "Computing prime divisors in an interval." Mathematics of Computation 84, no. 291 (2014): 339–54. http://dx.doi.org/10.1090/s0025-5718-2014-02840-8.

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4

Kloks, Ton, Jan Kratochvíl, and Haiko Müller. "Computing the branchwidth of interval graphs." Discrete Applied Mathematics 145, no. 2 (2005): 266–75. http://dx.doi.org/10.1016/j.dam.2004.01.015.

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5

Maier, R. W., J. F. Brennecke, and M. A. Stadtherr. "Computing Homogeneous Azeotropes Using Interval Analysis." Chemical Engineering & Technology 22, no. 12 (1999): 1063–67. http://dx.doi.org/10.1002/(sici)1521-4125(199912)22:12<1063::aid-ceat1063>3.0.co;2-z.

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6

Nagy, Benedek, and Sándor Vályi. "Circular Interval-valued Computers and Simulation of (Red-green) Turing Machines." Fundamenta Informaticae 181, no. 2-3 (2021): 213–38. http://dx.doi.org/10.3233/fi-2021-2057.

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Interval-valued computing is a kind of massively parallel computing. It operates on specific subsets of the interval [0,1) – unions of subintervals. They serve as basic data units and are called interval-values. It was established in [9], by a rather simple observation, that interval-valued computing, as a digital computing model, has computing power equivalent to Turing machines. However, this equivalence involves an unlimited number of interval-valued variables. In [14], the equivalence with Turing machines is established using a simulation that uses only a fixed number of interval-valued va

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7

Senn, Christoph Walter, and Itsuo Kumazawa. "Abstract Reservoir Computing." AI 3, no. 1 (2022): 194–210. http://dx.doi.org/10.3390/ai3010012.

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Noise of any kind can be an issue when translating results from simulations to the real world. We suddenly have to deal with building tolerances, faulty sensors, or just noisy sensor readings. This is especially evident in systems with many free parameters, such as the ones used in physical reservoir computing. By abstracting away these kinds of noise sources using intervals, we derive a regularized training regime for reservoir computing using sets of possible reservoir states. Numerical simulations are used to show the effectiveness of our approach against different sources of errors that ca

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8

Gillner, Lorenz, and Ekaterina Auer. "GPU-Accelerated, Interval-Based Parameter Identification Methods Illustrated Using the Two-Compartment Problem." Acta Cybernetica 26, no. 4 (2024): 913–32. https://doi.org/10.14232/actacyb.306774.

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Interval methods are helpful in the context of scientific computing for reliable treatment of problems with bounded uncertainty. Most traditional interval algorithms, however, were designed for sequential execution while internally depending on processor-specific instructions for directed rounding. Nowadays, many-core processors and dedicated hardware for massively parallel data processing have become the de facto standard for high-performance computers. Interval libraries have yet to adapt to this heterogeneous computing paradigm. In this article, we investigate the parallelization of interva

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9

Guan, Qing, and Jian He Guan. "Knowledge Acquisition of Interval Set-Valued Based on Granular Computing." Applied Mechanics and Materials 543-547 (March 2014): 2017–23. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.2017.

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The technique of a new extension of fuzzy rough theory using partition of interval set-valued is proposed for granular computing during knowledge discovery in this paper. The natural intervals of attribute values in decision system to be transformed into multiple sub-interval of [0,1]are given by normalization. And some characteristics of interval set-valued of decision systems in fuzzy rough set theory are discussed. The correctness and effectiveness of the approach are shown in experiments. The approach presented in this paper can also be used as a data preprocessing step for other symbolic

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10

Bustince, Humberto. "Interval-valued Fuzzy Sets in Soft Computing." International Journal of Computational Intelligence Systems 3, no. 2 (2010): 215. http://dx.doi.org/10.2991/ijcis.2010.3.2.9.

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11

Nagy, Benedek, and Sándor Vályi. "Computing discrete logarithm by interval-valued paradigm." Electronic Proceedings in Theoretical Computer Science 143 (March 29, 2014): 76–86. http://dx.doi.org/10.4204/eptcs.143.7.

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12

Bustince, Humberto. "Interval-valued Fuzzy Sets in Soft Computing." International Journal of Computational Intelligence Systems 3, no. 2 (2010): 215–22. http://dx.doi.org/10.1080/18756891.2010.9727692.

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13

Jin, Yan, and Jiang Hong Ma. "An Interval Slope Approach to Fuzzy C-Means Clustering Algorithm for Interval Valued Data." Advanced Materials Research 989-994 (July 2014): 1641–45. http://dx.doi.org/10.4028/www.scientific.net/amr.989-994.1641.

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Interval data is a range of continuous values which can describe the uncertainty. The traditional clustering methods ignore the structure information of intervals. And some modified ones have been developed. We have already used Taylor technique to perform well in the fuzzy c-means clustering algorithm. In this paper, we propose a new way based on the mixed interval slopes technique and interval computing. Experimental results also show the effectiveness of our approach.

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14

Hend, Dawood. "On Some Algebraic and Order-Theoretic Aspects of Machine Interval Arithmetic." Online Mathematics Journal 01, no. 02 (2019): 1–13. https://doi.org/10.5281/zenodo.2656089.

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Interval arithmetic is a fundamental and reliable mathematical machinery for scientific computing and for addressing uncertainty in general. In order to apply interval mathematics to real life uncertainty problems, one needs a computerized (machine) version thereof, and so, this article is devoted to some mathematical notions concerning the algebraic system of machine interval arithmetic. After formalizing some purely mathematical ingredients of particular importance for the purpose at hand, we give formal characterizations of the algebras of real intervals and machine intervals along with des

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15

Horáček, Jaroslav, Milan Hladík, and Josef Matějka. "Determinants of Interval Matrices." Electronic Journal of Linear Algebra 33 (May 16, 2018): 99–112. http://dx.doi.org/10.13001/1081-3810.3719.

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In this paper we shed more light on determinants of real interval matrices. Computing the exact bounds on a determinant of an interval matrix is an NP-hard problem. Therefore, attention is first paid to approximations. NP-hardness of both relative and absolute approximation is proved. Next, methods computing verified enclosures of interval determinants and their possible combination with preconditioning are discussed. A new method based on Cramer's rule was designed. It returns similar results to the state-of-the-art method, however, it is less consuming regarding computational time. Other met

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16

Nepomuceno, Erivelton G., Márcia L. C. Peixoto, Samir A. M. Martins, Heitor M. Rodrigues, and Matjaž Perc. "Inconsistencies in Numerical Simulations of Dynamical Systems Using Interval Arithmetic." International Journal of Bifurcation and Chaos 28, no. 04 (2018): 1850055. http://dx.doi.org/10.1142/s0218127418500554.

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Over the past few decades, interval arithmetic has been attracting widespread interest from the scientific community. With the expansion of computing power, scientific computing is encountering a noteworthy shift from floating-point arithmetic toward increased use of interval arithmetic. Notwithstanding the significant reliability of interval arithmetic, this paper presents a theoretical inconsistency in a simulation of dynamical systems using a well-known implementation of arithmetic interval. We have observed that two natural interval extensions present an empty intersection during a finite

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17

Lee, Youngjo, and Justus Seely. "Computing the Wald Interval for a Variance Ratio." Biometrics 52, no. 4 (1996): 1486. http://dx.doi.org/10.2307/2532863.

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18

Ting, Chao-Chun, and Min-Sheng Lin. "Computing 2-terminal reliability of probe interval graphs." Applied Mathematical Sciences 9 (2015): 419–27. http://dx.doi.org/10.12988/ams.2015.410883.

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19

Ferson, Scott, Lev Ginzburg, Vladik Kreinovich, Luc Longpré, and Monica Aviles. "Computing variance for interval data is NP-hard." ACM SIGACT News 33, no. 2 (2002): 108–18. http://dx.doi.org/10.1145/564585.564604.

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20

Spadoni, Massimo, and Luciano Stefanini. "Computing the variance of interval and fuzzy data." Fuzzy Sets and Systems 165, no. 1 (2011): 24–36. http://dx.doi.org/10.1016/j.fss.2010.09.003.

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21

Dankelmann, Peter. "Computing the average distance of an interval graph." Information Processing Letters 48, no. 6 (1993): 311–14. http://dx.doi.org/10.1016/0020-0190(93)90174-8.

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22

Zhang, Xian, Jianfeng Cai, and Yimin Wei. "Interval iterative methods for computing Moore–Penrose inverse." Applied Mathematics and Computation 183, no. 1 (2006): 522–32. http://dx.doi.org/10.1016/j.amc.2006.05.098.

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23

Mendel, Jerry M., and Mohammad Reza Rajati. "On Computing Normalized Interval Type-2 Fuzzy Sets." IEEE Transactions on Fuzzy Systems 22, no. 5 (2014): 1335–40. http://dx.doi.org/10.1109/tfuzz.2013.2280133.

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24

Chmiel, Wojciech, Iwona Skalna, and Stanisław Jędrusik. "Intelligent route planning system based on interval computing." Multimedia Tools and Applications 78, no. 4 (2018): 4693–721. http://dx.doi.org/10.1007/s11042-018-6714-x.

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25

Buckner, Gregory D., Heeju Choi, and Nathan S. Gibson. "Estimating Model Uncertainty using Confidence Interval Networks: Applications to Robust Control." Journal of Dynamic Systems, Measurement, and Control 128, no. 3 (2005): 626–35. http://dx.doi.org/10.1115/1.2199855.

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Robust control techniques require a dynamic model of the plant and bounds on model uncertainty to formulate control laws with guaranteed stability. Although techniques for modeling dynamic systems and estimating model parameters are well established, very few procedures exist for estimating uncertainty bounds. In the case of H∞ control synthesis, a conservative weighting function for model uncertainty is usually chosen to ensure closed-loop stability over the entire operating space. The primary drawback of this conservative, “hard computing” approach is reduced performance. This paper demonstr

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26

Chen, Chen-Tung, Kuan-Hung Lin, and Hui-Ling Cheng. "Computing the weights of criteria with interval-valued fuzzy sets for MCDM problems." International Journal of Engineering Research and Science 3, no. 9 (2017): 51–57. http://dx.doi.org/10.25125/engineering-journal-ijoer-sep-2017-19.

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27

Banachowicz, Andrzej, and Adam Wolski. "Interval Analysis of Navigational Problems / Analiza Przedziałowa Zadań Nawigacyjnych." Journal of KONBiN 22, no. 1 (2012): 89–96. http://dx.doi.org/10.2478/jok-2013-0024.

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Abstract Algorithms of solutions to navigational problems usually comprise elements for numerical calculations. Apart from random errors, numerical errors of varying nature can be found in them. These errors are due to the level of precision of input data, the approximability of computing methods and errors generated by the computing very process itself in a computer. The latter category includes numerical precision (floating point of a numerical notation) and rounding off of numbers. These errors are analyzed as absolute and relative errors, rounding off errors and are regarded as random erro

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28

Libo, Xu, Li Xingsen, Pang Chaoyi, and Guo Yan. "Simplified Neutrosophic Sets Based on Interval Dependent Degree for Multi-Criteria Group Decision-Making Problems." Symmetry 10, no. 11 (2018): 640. http://dx.doi.org/10.3390/sym10110640.

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In this paper, a new approach and framework based on the interval dependent degree for multi-criteria group decision-making (MCGDM) problems with simplified neutrosophic sets (SNSs) is proposed. Firstly, the simplified dependent function and distribution function are defined. Then, they are integrated into the interval dependent function which contains interval computing and distribution information of the intervals. Subsequently, the interval transformation operator is defined to convert simplified neutrosophic numbers (SNNs) into intervals, and then the interval dependent function for SNNs i

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29

Witkovsky, Viktor. "On the Exact Two-Sided Tolerance Intervals for Univariate Normal Distribution and Linear Regression." Austrian Journal of Statistics 43, no. 4 (2014): 279–92. http://dx.doi.org/10.17713/ajs.v43i4.46.

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Statistical tolerance intervals are another tool for making statistical inference on anunknown population. The tolerance interval is an interval estimator based on the resultsof a calibration experiment, which can be asserted with stated confidence level 1 ? ,for example 0.95, to contain at least a specified proportion 1 ? , for example 0.99, ofthe items in the population under consideration. Typically, the limits of the toleranceintervals functionally depend on the tolerance factors. In contrast to other statisticalintervals commonly used for statistical inference, the tolerance intervals are

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30

Robinson, P. John, and E. C. Henry Amirtharaj. "Vague Correlation Coefficient of Interval Vague Sets." International Journal of Fuzzy System Applications 2, no. 1 (2012): 18–34. http://dx.doi.org/10.4018/ijfsa.2012010102.

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Various attempts have been made by researchers on the study of vagueness of data through intuitionistic fuzzy sets and vague sets, and also it was shown that vague sets are intuitionistic fuzzy sets. But there are algebraic and graphical differences between vague sets and intuitionistic fuzzy sets. In this paper an attempt is made to define the correlation coefficient of interval vague sets lying in the interval [0, 1], and a new method for computing the correlation coefficient of interval vague sets lying in the interval [-1, 1] using a-cuts over the vague degrees through statistical confiden

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31

Qi, Bin, Jie Ma, and Kewei Lv. "Computing Interval Discrete Logarithm Problem with Restricted Jump Method." Fundamenta Informaticae 177, no. 2 (2020): 189–201. http://dx.doi.org/10.3233/fi-2020-1986.

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The interval discrete logarithm problem(IDLP) is to find a solution n such that gn = h in a finite cyclic group G = 〈g〉, where h ∈ G and n belongs to a given interval. To accelerate solving IDLP, a restricted jump method is given to speed up Pollard’s kangaroo algorithm in this paper. Since the Pollard’ kangaroo-like method need to compute the intermediate value during every iteration, the restricted jump method gives another way to reuse the intermediate value so that each iteration is speeded up at least 10 times. Actually, there are some variants of kangaroo method pre-compute the intermedi

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32

He, Ling T., Chenyi Hu, and K. Michael Casey. "Prediction of variability in mortgage rates: interval computing solutions." Journal of Risk Finance 10, no. 2 (2009): 142–54. http://dx.doi.org/10.1108/15265940910938224.

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33

Zhang, Xiaoping, and Jin Li. "Composite trapezoidal quadrature for computing hypersingular integrals on interval." AIMS Mathematics 9, no. 12 (2024): 34537–66. https://doi.org/10.3934/math.20241645.

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<p>In this paper, composite trapezoidal quadrature for numerical evaluation of hypersingular integrals was first introduced. By Taylor expansion at the singular point $ y $, error functional was obtained. We know that the divergence rate of $ O(h^{-p}), p = 1, 2 $, and there were no roots of the special function for the first part in the error functional. Meanwhile, for the second part of the error functional, the divergence rate was $ O(h^{-p+1}), p = 1, 2 $, but there were roots of the special function. We proved that the convergence rate could reach $ O(h^{2}) $ at superconvergence po

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34

Hemaspaandra, Lane A., Christopher M. Homan, Sven Kosub, and Klaus W. Wagner. "The Complexity of Computing the Size of an Interval." SIAM Journal on Computing 36, no. 5 (2007): 1264–300. http://dx.doi.org/10.1137/s0097539705447013.

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35

Anderson-Bergman, Clifford, and Yaming Yu. "Computing the log concave NPMLE for interval censored data." Statistics and Computing 26, no. 4 (2015): 813–26. http://dx.doi.org/10.1007/s11222-015-9571-8.

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36

He, Ling T., and Chenyi Hu. "Impacts of Interval Computing on Stock Market Variability Forecasting." Computational Economics 33, no. 3 (2008): 263–76. http://dx.doi.org/10.1007/s10614-008-9159-x.

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37

Danielson, Mats, and Love Ekenberg. "Computing upper and lower bounds in interval decision trees." European Journal of Operational Research 181, no. 2 (2007): 808–16. http://dx.doi.org/10.1016/j.ejor.2006.06.030.

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38

Wang, Renhong, and Xiaolei Zhang. "Interval iterative algorithm for computing the piecewise algebraic variety." Computers & Mathematics with Applications 56, no. 2 (2008): 565–71. http://dx.doi.org/10.1016/j.camwa.2008.01.036.

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39

Carlborg, O. "Parallel Computing in Interval Mapping of Quantitative Trait Loci." Journal of Heredity 92, no. 5 (2001): 449–51. http://dx.doi.org/10.1093/jhered/92.5.449.

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40

Chan, Ting Pong, and Rao S. Govindaraju. "Interval Computing Method for Analyzing Field-Scale Solute Transport." Journal of Hydrologic Engineering 6, no. 6 (2001): 480–89. http://dx.doi.org/10.1061/(asce)1084-0699(2001)6:6(480).

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41

Mendel, J. M. "Computing Derivatives in Interval Type-2 Fuzzy Logic Systems." IEEE Transactions on Fuzzy Systems 12, no. 1 (2004): 84–98. http://dx.doi.org/10.1109/tfuzz.2003.822681.

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42

Krämer, Walter. "Computing and Visualizing Solution Sets of Interval Linear Systems." Serdica Journal of Computing 1, no. 4 (2007): 455–68. http://dx.doi.org/10.55630/sjc.2007.1.455-468.

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The computation of the exact solution set of an interval linear system is a nontrivial task [2, 13]. Even in two and three dimensions a lot of work has to be done. We demonstrate two different realizations. The first approach (see [16]) is based on Java, Java3D, and the BigRational package [21]. An applet allows modifications of the matrix coefficients and/or the coefficients of the right hand side with concurrent real time visualization of the corresponding solution sets. The second approach (see [5]) uses Maple and intpakX [22, 8, 12] to implement routines for the computation and visualizati

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43

Wang, Jizhong, Jin Li, and Yueting Zhou. "The trapezoidal rule for computing supersingular integral on interval." Applied Mathematics and Computation 219, no. 4 (2012): 1616–24. http://dx.doi.org/10.1016/j.amc.2012.08.003.

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44

Leng, Huinan, Zhiqing He, and Quan Yuan. "Computing bounds to real eigenvalues of real-interval matrices." International Journal for Numerical Methods in Engineering 74, no. 4 (2007): 523–30. http://dx.doi.org/10.1002/nme.2179.

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45

Hartman, David, Milan Hladík, and David Říha. "Computing the spectral decomposition of interval matrices and a study on interval matrix powers." Applied Mathematics and Computation 403 (August 2021): 126174. http://dx.doi.org/10.1016/j.amc.2021.126174.

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46

DILÃO, RUI, and JOSÉ AMIGÓ. "COMPUTING THE TOPOLOGICAL ENTROPY OF UNIMODAL MAPS." International Journal of Bifurcation and Chaos 22, no. 06 (2012): 1250152. http://dx.doi.org/10.1142/s0218127412501520.

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We derive an algorithm to determine recursively the lap number (minimal number of monotone pieces) of the iterates of unimodal maps of an interval with free end-points. For this family of maps, the kneading sequence does not determine the lap numbers. The algorithm is obtained by the sign analysis of the itineraries of the critical point and of the boundary points of the interval map. We apply this algorithm to the estimation of the growth number and the topological entropy of maps with direct and reverse bifurcations.

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47

Nishimura, Maki, Wataru Namiki, Daiki Nishioka, Kazuya Terabe, and Takashi Tsuchiya. "Optimization of Reservoir Computing Utilizing Interfered Spin Waves." ECS Meeting Abstracts MA2024-02, no. 48 (2024): 3385. https://doi.org/10.1149/ma2024-02483385mtgabs.

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Reservoir computing is a learning model that enables low-cost and fast learning compared to conventional deep learning. It enables physical implementation by replacing the reservoir part with a physical device that possesses nonlinearity, short-term memory, and high dimensionality. In particular, it was theoretically predicted that spin wave interference can perform highly efficient reservoir computing in micromagnetic simulations,[1] and it was experimentally verified by the present authors.[2] Whereas the computational performance was suggested to vary significantly depending on the interval

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48

Utkin, Lev V. "Imprecise Second-Order Hierarchical Uncertainty Model." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 11, no. 03 (2003): 301–17. http://dx.doi.org/10.1142/s0218488503002090.

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A hierarchical uncertainty model for combining different evidence is studied in the paper. The model is general enough for many applications. The presented approach for dealing with the model allows us to combine the available heterogeneous information in the following ways: computing new probability bounds for some predefined interval of previsions, computing an "average" interval of first-order previsions, and updating the second-order probabilities after observing new events. Numerical examples illustrate this approach.

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49

GAVRILOVA, M., and J. ROKNE. "COMPUTING LINE INTERSECTIONS." International Journal of Image and Graphics 01, no. 02 (2001): 217–30. http://dx.doi.org/10.1142/s0219467801000141.

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The main result of the paper is a new and efficient algorithm to compute the closest possible representable intersection point between two lines in the plane. The coordinates of the points that define the lines are given as single precision floating-point numbers. The novelty of the algorithm is the method for deriving the best possible representable floating point numbers: instead of solving the equations to compute the line intersection coordinates exactly, which is a computationally expensive procedure, an iterative binary search procedure is applied. When the required precision is achieved

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50

UTKIN, LEV V. "CAUTIOUS ANALYSIS OF PROJECT RISKS BY INTERVAL-VALUED INITIAL DATA." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 14, no. 06 (2006): 663–85. http://dx.doi.org/10.1142/s0218488506004266.

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One of the most common performance measures in selection and management of projects is the Net Present Value (NPV). In the paper, we study a case when initial data about the NPV parameters (cash flows and the discount rate) are represented in the form of intervals supplied by experts. A method for computing the NPV based on using random set theory is proposed and three conditions of independence of the parameters are taken into account. Moreover, the imprecise Dirichlet model for obtaining more cautious bounds for the NPV is considered. Numerical examples illustrate the proposed approach for c

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