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Journal articles on the topic 'Rounding error analysis'

Author: Grafiati

Published: 25 May 2024

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1

Connolly, Michael P., and Nicholas J. Higham. "Probabilistic Rounding Error Analysis of Householder QR Factorization." SIAM Journal on Matrix Analysis and Applications 44, no. 3 (2023): 1146–63. http://dx.doi.org/10.1137/22m1514817.

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2

Kolomys, Olena, and Liliya Luts. "Algorithm for Calculating Primary Spectral Density Estimates Using FFT and Analysis of its Accuracy." Cybernetics and Computer Technologies, no. 2 (September 30, 2022): 52–57. http://dx.doi.org/10.34229/2707-451x.22.2.5.

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Introduction. Fast algorithms for solving problems of spectral and correlation analysis of random processes began to appear mainly after 1965, when the algorithm of fast Fourier transform (FFT) entered computational practice. With its appearance, a number of computational algorithms for the accelerated solution of some problems of digital signal processing were developed, speed-efficient algorithms for calculating such estimates of probabilistic characteristics of control objects as estimates of convolutions, correlation functions, spectral densities of stationary and some types of non-station

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3

Connolly, Michael P., Nicholas J. Higham, and Theo Mary. "Stochastic Rounding and Its Probabilistic Backward Error Analysis." SIAM Journal on Scientific Computing 43, no. 1 (2021): A566—A585. http://dx.doi.org/10.1137/20m1334796.

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4

Cuyt, Annie, and Paul Van der Cruyssen. "Rounding error analysis for forward continued fraction algorithms." Computers & Mathematics with Applications 11, no. 6 (1985): 541–64. http://dx.doi.org/10.1016/0898-1221(85)90037-9.

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Higham, Nicholas J., and Theo Mary. "A New Approach to Probabilistic Rounding Error Analysis." SIAM Journal on Scientific Computing 41, no. 5 (2019): A2815—A2835. http://dx.doi.org/10.1137/18m1226312.

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6

Zou, Qinmeng. "Probabilistic Rounding Error Analysis of Modified Gram–Schmidt." SIAM Journal on Matrix Analysis and Applications 45, no. 2 (2024): 1076–88. http://dx.doi.org/10.1137/23m1585817.

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7

Mezzarobba, Marc. "Rounding error analysis of linear recurrences using generating series." ETNA - Electronic Transactions on Numerical Analysis 58 (2023): 196–227. http://dx.doi.org/10.1553/etna_vol58s196.

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8

Kiełbasiński, Andrzej. "A note on rounding-error analysis of Cholesky factorization." Linear Algebra and its Applications 88-89 (April 1987): 487–94. http://dx.doi.org/10.1016/0024-3795(87)90121-2.

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9

Journal, Baghdad Science. "A Note on the Perturbation of arithmetic expressions." Baghdad Science Journal 13, no. 1 (2016): 190–97. http://dx.doi.org/10.21123/bsj.13.1.190-197.

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In this paper we present the theoretical foundation of forward error analysis of numerical algorithms under;• Approximations in "built-in" functions.• Rounding errors in arithmetic floating-point operations.• Perturbations of data.The error analysis is based on linearization method. The fundamental tools of the forward error analysis are system of linear absolute and relative a prior and a posteriori error equations and associated condition numbers constituting optimal of possible cumulative round – off errors. The condition numbers enable simple general, quantitative bounds definitions of num

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Rudikov, D. A., and A. S. Ilinykh. "Error analysis of the cutting machine step adjustable drive." Journal of Physics: Conference Series 2131, no. 2 (2021): 022046. http://dx.doi.org/10.1088/1742-6596/2131/2/022046.

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Abstract The implementation precision of a number of adjustment bodies of a metal-cutting machine is also the most important indicator of its quality, a strictly standardized industry standard, technical conditions for manufacturing and acceptance. Moreover, the standard for limiting the error is set depending on the used denominator of the series. An essential feature of the precision of the series being implemented is that it is determined not by an error in parts’ manufacturing, but by the disadvantages of the used method of kinematic calculation. The established modes largely determine the

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11

Paxton, E. Adam, Matthew Chantry, Milan Klöwer, Leo Saffin, and Tim Palmer. "Climate Modeling in Low Precision: Effects of Both Deterministic and Stochastic Rounding." Journal of Climate 35, no. 4 (2022): 1215–29. http://dx.doi.org/10.1175/jcli-d-21-0343.1.

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Abstract Motivated by recent advances in operational weather forecasting, we study the efficacy of low-precision arithmetic for climate simulations. We develop a framework to measure rounding error in a climate model, which provides a stress test for a low-precision version of the model, and we apply our method to a variety of models including the Lorenz system, a shallow water approximation for flow over a ridge, and a coarse-resolution spectral global atmospheric model with simplified parameterizations (SPEEDY). Although double precision [52 significant bits (sbits)] is standard across opera

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12

Yang, L. Minah, Alyson Fox, and Geoffrey Sanders. "Rounding Error Analysis of Mixed Precision Block Householder QR Algorithms." SIAM Journal on Scientific Computing 43, no. 3 (2021): A1723—A1753. http://dx.doi.org/10.1137/19m1296367.

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13

Neumaier, A. "Inner product rounding error analysis in the presence of underflow." Computing 34, no. 4 (1985): 365–73. http://dx.doi.org/10.1007/bf02251835.

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14

Giraud, Luc, Julien Langou, Miroslav Rozložník, and Jasper van den Eshof. "Rounding error analysis of the classical Gram-Schmidt orthogonalization process." Numerische Mathematik 101, no. 1 (2005): 87–100. http://dx.doi.org/10.1007/s00211-005-0615-4.

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15

Iiguni, Youji, Hideaki Sakai, and Hidekatsu Tokumaru. "Rounding error analysis of the triangular lattice and escalator algorithms." Electronics and Communications in Japan (Part I: Communications) 71, no. 4 (1988): 15–25. http://dx.doi.org/10.1002/ecja.4410710402.

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16

Holstein, Horst, and Ben Ketteridge. "Gravimetric analysis of uniform polyhedra." GEOPHYSICS 61, no. 2 (1996): 357–64. http://dx.doi.org/10.1190/1.1443964.

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Analytical formulas for the gravity anomaly of a uniform polyhedral body are subject to numerical error that increases with distance from the target, while the anomaly decreases. This leads to a limited range of target distances in which the formulas are operational, beyond which the calculations are dominated by rounding error. We analyze the sources of error and propose a combination of numerical and analytical procedures that exhibit advantages over existing methods, namely (1) errors that diminish with distance, (2) enhanced operating range, and (3) algorithmic simplicity. The latter is ac

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17

Wang, Miao, Weifeng Liu, and Chenglin Wen. "A High-Order Kalman Filter Method for Fusion Estimation of Motion Trajectories of Multi-Robot Formation." Sensors 22, no. 15 (2022): 5590. http://dx.doi.org/10.3390/s22155590.

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Multi-robot motion and observation generally have nonlinear characteristics; in response to the problem that the existing extended Kalman filter (EKF) algorithm used in robot position estimation only considers first-order expansion and ignores the higher-order information, this paper proposes a multi-robot formation trajectory based on the high-order Kalman filter method. The joint estimation method uses Taylor expansion of the state equation and observation equation and introduces remainder variables on this basis, which effectively improves the estimation accuracy. In addition, the truncatio

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18

Lu, Mi. "Runtime accuracy alterable approximate floatingpoint multipliers." International Robotics & Automation Journal 8, no. 2 (2022): 52–56. http://dx.doi.org/10.15406/iratj.2022.08.00244.

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Modern systems demand high computational power within limited resources. Approximate computing is a promising approach to design arithmetic units with tight resources for error-tolerant applications such as image and signal processing and computer vision. A floating-point multiplier is one of the arithmetic units with the highest complexity in such applications. Designing a floating-point multiplier based on the approximate computing technique can reduce its complexity as well as increase performance and energy efficiency. However, an unknown error rate for upcoming input data is problematic t

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19

Singer, Sanja, and Saša Singer. "Rounding-error and perturbation bounds for the indefinite QR factorization." Linear Algebra and its Applications 309, no. 1-3 (2000): 103–19. http://dx.doi.org/10.1016/s0024-3795(99)00156-1.

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20

Singer, Sanja, and Saša Singer. "Rounding error and perturbation bounds for the symplectic QR factorization." Linear Algebra and its Applications 358, no. 1-3 (2003): 255–79. http://dx.doi.org/10.1016/s0024-3795(02)00263-x.

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21

Cao, Zhi-Hao. "Rounding error analysis of two-stage iterative methods for large linear systems." Applied Mathematics and Computation 139, no. 2-3 (2003): 371–81. http://dx.doi.org/10.1016/s0096-3003(02)00201-1.

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22

Yang, Fan, Songlin Liu, Yijun Lai, Jiayuan Hu, and Shaohua Wang. "An Improved Magnetic Field Method to Locate the Grounding Conductor." Sensors 23, no. 8 (2023): 3879. http://dx.doi.org/10.3390/s23083879.

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The location of the grounding grid conductors is critical for performing corrosion diagnosis and maintenance work. An improved magnetic field differential method to locate the unknown grounding grid based on truncation errors and the round-off errors analysis is presented in this paper. It was proven that a different order of the magnetic field derivative can be used to determine the position of the grounding conductor according to the peak value of the derivative. Due to the accumulative error of higher differentiation, the truncation error and rounding error were used to analyze to accumulat

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23

Korzilius, Stan, and Berry Schoenmakers. "Divisions and Square Roots with Tight Error Analysis from Newton–Raphson Iteration in Secure Fixed-Point Arithmetic." Cryptography 7, no. 3 (2023): 43. http://dx.doi.org/10.3390/cryptography7030043.

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In this paper, we present new variants of Newton–Raphson-based protocols for the secure computation of the reciprocal and the (reciprocal) square root. The protocols rely on secure fixed-point arithmetic with arbitrary precision parameterized by the total bit length of the fixed-point numbers and the bit length of the fractional part. We perform a rigorous error analysis aiming for tight accuracy claims while minimizing the overall cost of the protocols. Due to the nature of secure fixed-point arithmetic, we perform the analysis in terms of absolute errors. Whenever possible, we allow for stoc

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24

Chesnel, Lucas, Xavier Claeys, and Sergei A. Nazarov. "Oscillating behaviour of the spectrum for a plasmonic problem in a domain with a rounded corner." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 4 (2018): 1285–313. http://dx.doi.org/10.1051/m2an/2016080.

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We investigate the eigenvalue problem −div(σ∇u) = λu (P) in a 2D domain Ω divided into two regions Ω±. We are interested in situations where σ takes positive values on Ω+ and negative ones on Ω−. Such problems appear in time harmonic electromagnetics in the modeling of plasmonic technologies. In a recent work [L. Chesnel, X. Claeys and S.A. Nazarov, Asymp. Anal. 88 (2014) 43–74], we highlighted an unusual instability phenomenon for the source term problem associated with (P): for certain configurations, when the interface between the subdomains Ω± presents a rounded corner, the solution may de

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25

Gemignani, Luca, and Grazia Lotti. "Rounding Error Analysis in Solving M-Matrix Linear Systems of Block Hessenberg Form." Numerical Algorithms 36, no. 2 (2004): 157–68. http://dx.doi.org/10.1023/b:numa.0000033130.75020.0e.

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26

Wang, Weijie, and Yanmin Lu. "Analysis of the Mean Absolute Error (MAE) and the Root Mean Square Error (RMSE) in Assessing Rounding Model." IOP Conference Series: Materials Science and Engineering 324 (March 2018): 012049. http://dx.doi.org/10.1088/1757-899x/324/1/012049.

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27

Maryška, J., M. Rozložnı́k, and M. Tůma. "Schur complement reduction in the mixed-hybrid approximation of Darcy's law: rounding error analysis." Journal of Computational and Applied Mathematics 117, no. 2 (2000): 159–73. http://dx.doi.org/10.1016/s0377-0427(99)00344-1.

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28

Goede, Simon L., and Melvin Khee-Shing Leow. "General Error Analysis in the Relationship between Free Thyroxine and Thyrotropin and Its Clinical Relevance." Computational and Mathematical Methods in Medicine 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/831275.

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Background. This treatise investigates error sources in measurements applicable to the hypothalamus-pituitary-thyroid (HPT) system of analysis for homeostatic set point computation. The hypothalamus-pituitary transfer characteristic (HP curve) describes the relationship between plasma free thyroxine [FT4] and thyrotropin [TSH].Objective. We define the origin, types, causes, and effects of errors that are commonly encountered in TFT measurements and examine how we can interpret these to construct a reliable HP function for set point establishment.Design and Methods. The error sources in the cli

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29

Erna, G., G. Srihari, M. Purna Kishore, Ashok Nayak B., and M. Bharathi. "FPGA Implementation of High-Performance Truncated Rounding based Approximate Multiplier with High-Level Synchronous XOR-MUX Full Adder." WSEAS TRANSACTIONS ON CIRCUITS AND SYSTEMS 22 (December 4, 2023): 111–25. http://dx.doi.org/10.37394/23201.2023.22.13.

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In research and development, the most emerging field in digital signal processing and image processing is rounded-based approximated signed and unsigned multipliers. In the present research, we propose some cutting-edge, Preformation, and logic simplification technology connected to processing the Discrete cosine transform (DCT) and Discrete wavelet transform (DWT) images for sharpening. This technology will yield a truncated shifter incorporated with logical XOR-MUX Full adder techniques. A reliable and cost-effective approximate signed and unsigned multiplier was created for the rounding met

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30

Stolwijk, Jeroen J., and Volker Mehrmann. "Error Analysis and Model Adaptivity for Flows in Gas Networks." Analele Universitatii "Ovidius" Constanta - Seria Matematica 26, no. 2 (2018): 231–66. http://dx.doi.org/10.2478/auom-2018-0027.

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Abstract In the simulation and optimization of natural gas flow in a pipeline network, a hierarchy of models is used that employs different formulations of the Euler equations. While the optimization is performed on piecewise linear models, the flow simulation is based on the one to three dimensional Euler equations including the temperature distributions. To decide which model class in the hierarchy is adequate to achieve a desired accuracy, this paper presents an error and perturbation analysis for a two level model hierarchy including the isothermal Euler equations in semilinear form and th

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31

Cools, Siegfried, Emrullah Fatih Yetkin, Emmanuel Agullo, Luc Giraud, and Wim Vanroose. "Analyzing the Effect of Local Rounding Error Propagation on the Maximal Attainable Accuracy of the Pipelined Conjugate Gradient Method." SIAM Journal on Matrix Analysis and Applications 39, no. 1 (2018): 426–50. http://dx.doi.org/10.1137/17m1117872.

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32

Baber, William R., and Sok-Hyon Kang. "The Impact of Split Adjusting and Rounding on Analysts' Forecast Error Calculations." Accounting Horizons 16, no. 4 (2002): 277–89. http://dx.doi.org/10.2308/acch.2002.16.4.277.

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This study finds that analysts' forecast data files, commonly used by accountants and financial analysts to estimate market expectations about earnings announcements, contain inaccurate historical data for companies that split their common stock. These inaccuracies result because stock split adjustments are made retrospectively and split-adjusted data are rounded. Moreover, because well-performing firms are more likely to execute stock splits, the consequences of the stock split problem are systematic, potentially distorting both time-series and cross-sectional characteristics of forecast erro

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33

Wang, Dong Xing, and Su Chen. "Improved Subdivision Based Halftoning Algorithm." Advanced Materials Research 267 (June 2011): 368–71. http://dx.doi.org/10.4028/www.scientific.net/amr.267.368.

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The subdivision based halftoning algorithm works in a statistical way. Analysis of its output shows that, error accumulation and rounding operation may produce big quantization error, and there may be artifacts in its output. Some improvements have been proposed. First, a procedure is added to find cases with big quantization error, and to solve the problem. Second, instead of propagating error sequentially as in the algorithm, propagating error along random directions has been tested to reduce the artifacts in the output. Third, propagating error along a direction, in which the quantization e

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34

Guo, Haifeng, Yiyang Wang, Guangwei Wang, Zhongbo Du, Rui Chen, and He Sun. "Artificial Intelligence Optimization Design Analysis of Robot Control System." Journal of Sensors 2022 (July 25, 2022): 1–6. http://dx.doi.org/10.1155/2022/2235042.

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In order to improve the accuracy of robot control system, a scheme based on artificial intelligence is proposed. On the basis of the software environment of reinforcement learning simulation platform, a kind of rounding scheme in dynamic environment is designed and simulated. The results show that when the inclination sensor is placed on an inclined plane of 300 and collected for ten times, the maximum error of measurement that can be seen from the experimental data is 0.40. The relative included angles were 30°, 45°, 60°, and 90°, respectively, by compass sensor. The measurement was carried o

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35

Zylstra, Philip J., David B. Lindenmayer, and S. Don Bradshaw. "Reply to Comment on ‘Self-thinning forest understoreys reduce wildfire risk, even in a warming climate’." Environmental Research Letters 19, no. 5 (2024): 058001. http://dx.doi.org/10.1088/1748-9326/ad40c1.

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Abstract Our previous analysis of mapped records of forest fires in National Parks in Southwestern Australia showed that fires initiated a pulse in flammability (the likelihood of a point being burned by wildfire), but that flammability declined as forests matured (Zylstra et al 2022 Environ. Res. Lett. 17 044022). This reduction in flammability was contrary to that expected from modelling used by the West Australian Government to guide management, but consistent with expectations from peer-reviewed fire behaviour science and published ecological drivers of fire behaviour. Miller et al (2024 E

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36

Lemeshko, Boris Yu, and Stanislav B. Lemeshko. "Nonparametric goodness-of-fit tests for normality testing under rounding-off measurements." Analysis and data processing systems, no. 2 (June 28, 2022): 21–38. http://dx.doi.org/10.17212/2782-2001-2022-2-21-38.

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When analyzing measurement series in various applications, the verification of whether measurement errors belong to the normal law is considered as a mandatory procedure. For this purpose, various special tests for testing hypotheses about normality can be used; non-parametric tests of goodness or chi-square tests can be used. When using nonparametric goodness-of-fit tests to test normality, it must be taken into account that a complex hypothesis is being tested. When testing a complex hypothesis, the distributions of the statistics of the goodness-of-fit tests differ significantly from the cl

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37

Vijeyakumar, K. N., S. Elango, and S. Kalaiselvi. "VLSI Implementation of High Speed Energy-Efficient Truncated Multiplier." Journal of Circuits, Systems and Computers 27, no. 05 (2018): 1850077. http://dx.doi.org/10.1142/s0218126618500779.

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In this brief, we present the design and evaluation of a high speed and energy-efficient truncated multiplier for unsigned multiplication, such that the average absolute error due to truncation and rounding is kept minimal. The proposed algorithm eliminates a few least significant Partial Product (PP) bits and adds correction bias at appropriate PP bit positions to minimize the total error. From the literatures reviewed, it is clear that there is scope for reducing delay in multiplication using sutras of ancient vedic mathematics. This work uses a simple “crosswise and vertical sutra” of Vedic

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38

Xu, Chuan Yan, Kang Ding, Zhi Jian Yang, and Hui Bin Lin. "Influence of Additive White Gaussian Noise on the Interpolation Method of Discrete Spectrum." Advanced Materials Research 383-390 (November 2011): 2951–57. http://dx.doi.org/10.4028/www.scientific.net/amr.383-390.2951.

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Without noise, the interpolation method of discrete spectrum is accurate except rounding error. However, the estimation accuracy is declined when a signal corrupted with noise, and even turns out to be meaningless. The paper investigates the influence of additive White Gaussian Noise on the accuracy of amplitude and phase based on interpolation method. Analytical expressions of the estimator variance for amplitude and phase correction are derived. Simulation results confirm the validity of the presented analysis.

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39

Rahayu, Santi, and Achmad Hindasyah. "Comparative Analysis of Numerical Integration Solutions Pias Method and Newton Cotes Method Using Python Programming Language." Mathline : Jurnal Matematika dan Pendidikan Matematika 8, no. 4 (2023): 1321–32. http://dx.doi.org/10.31943/mathline.v8i4.492.

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Irregular areas cannot be solved by ordinary calculus formulas, so it is necessary to use numerical methods such as the Quadrature and Newton-Cotes methods. This research compares numerical integration solutions using the Quadrature method (Rectangular and Trapezoidal) and the Newton-Cotes method (Trapezoidal, Simpson 1/3, Simpson 3/8, and Weddle) with the Python programming language. Manual calculation of the first case study on integrals where the smallest error from the numerical method to the analytical method is achieved by the rectangular method of 0,017. In the second case study of tabu

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40

Seo, Jung-In, Young Eun Jeon, and Suk-Bok Kang. "New Approach for a Weibull Distribution under the Progressive Type-II Censoring Scheme." Mathematics 8, no. 10 (2020): 1713. http://dx.doi.org/10.3390/math8101713.

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This paper proposes a new approach based on the regression framework employing a pivotal quantity to estimate unknown parameters of a Weibull distribution under the progressive Type-II censoring scheme, which provides a closed form solution for the shape parameter, unlike its maximum likelihood estimator counterpart. To resolve serious rounding errors for the exact mean and variance of the pivotal quantity, two different types of Taylor series expansion are applied, and the resulting performance is enhanced in terms of the mean square error and bias obtained through the Monte Carlo simulation.

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41

de Camargo, André Pierro. "Rounding error analysis of divided differences schemes: Newton’s divided differences; Neville’s algorithm; Richardson extrapolation; Romberg quadrature; etc." Numerical Algorithms 85, no. 2 (2019): 591–606. http://dx.doi.org/10.1007/s11075-019-00828-1.

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42

Noeiaghdam, Samad, Aliona Dreglea, Jihuan He, et al. "Error Estimation of the Homotopy Perturbation Method to Solve Second Kind Volterra Integral Equations with Piecewise Smooth Kernels: Application of the CADNA Library." Symmetry 12, no. 10 (2020): 1730. http://dx.doi.org/10.3390/sym12101730.

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This paper studies the second kind linear Volterra integral equations (IEs) with a discontinuous kernel obtained from the load leveling and energy system problems. For solving this problem, we propose the homotopy perturbation method (HPM). We then discuss the convergence theorem and the error analysis of the formulation to validate the accuracy of the obtained solutions. In this study, the Controle et Estimation Stochastique des Arrondis de Calculs method (CESTAC) and the Control of Accuracy and Debugging for Numerical Applications (CADNA) library are used to control the rounding error estima

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43

Liu, Zhao-Guang, Sheng-Yong Du, Yang Yang, and Xiu-Hua Ji. "A fast algorithm for color space conversion and rounding error analysis based on fixed-point digital signal processors." Computers & Electrical Engineering 40, no. 4 (2014): 1405–14. http://dx.doi.org/10.1016/j.compeleceng.2013.01.011.

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44

Protsko, I. O., and D. V. Ostrovka. "ANALYSIS OF THE ERROR OF COMPUTATION FAST TRANSFORMS OF FOURIER CLASS BASED ON CYCLIC CONVOLUTIONS." Ukrainian Journal of Information Technology 2, no. 1 (2020): 52–56. http://dx.doi.org/10.23939/ujit2020.02.052.

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The features of the computational model of discrete transforms of Fourier class based on cyclic convolutions to determine the algorithmic calculation error are analyzed. Based on the approach of efficient computation of discrete transforms of Fourier class of arbitrary size N, using of a hashing array to transform a discrete basis matrix into a set of block-cyclic submatrices, the components of computational costs are considered. These components of computational costs depend on the type of transform, the size and the block-cycle structure of the transformation core. Examples of computational

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45

Zhou, H., Y. Zhang, J. Wen, and S. Cui. "Mould cooling simulation for injection moulding using a fast boundary element method approach." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 224, no. 4 (2009): 653–62. http://dx.doi.org/10.1243/09544054jem1407.

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The existing cooling simulations for injection moulding are mostly based on the boundary element method (BEM). In this paper, a fast BEM approach for mould cooling analysis is developed. The actual problem is decoupled into a one-dimensional transient heat conduction problem within the thin part and a cycle-averaged steady state three-dimensional heat conduction problem of the mould. The BEM is formulated for the solution of the mould heat transfer problem. A dynamic allocation strategy of integral points is proposed when using the Gaussian integral formula to generate the BEM matrix. Consider

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46

Lam, Michael O., and Jeffrey K. Hollingsworth. "Fine-grained floating-point precision analysis." International Journal of High Performance Computing Applications 32, no. 2 (2016): 231–45. http://dx.doi.org/10.1177/1094342016652462.

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Floating-point computation is ubiquitous in high-performance scientific computing, but rounding error can compromise the results of extended calculations, especially at large scales. In this paper, we present new techniques that use binary instrumentation and modification to do fine-grained floating-point precision analysis, simulating any level of precision less than or equal to the precision of the original program. These techniques have an average of 40–70% lower overhead and provide more fine-grained insights into a program’s sensitivity than previous mixed-precision analyses. We also pres

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47

Gao, Zhenyi, Bin Zhou, Chao Li, et al. "Design and Implementation of a System-on-Chip for Self-Calibration of an Angular Position Sensor." Applied Sciences 9, no. 22 (2019): 4772. http://dx.doi.org/10.3390/app9224772.

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In this study, a novel signal processing algorithm and hardware processing circuit for the self-calibration of angular position sensors is proposed. To calibrate error components commonly found in angular position sensors, a parameter identification algorithm based on the least mean square error demodulation is developed. A processor to run programs and a coprocessor based on the above algorithm are used and designed to form a System-on-Chip, which can calibrate signals as well as implement parameter configuration and control algorithm applications. In order to verify the theoretical validity

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Dhawalikar, Mahesh Narayan, V. Mariappan, P. K. Srividhya, and Vishal Kurtikar. "Multi-state failure phenomenon and analysis using semi-Markov model." International Journal of Quality & Reliability Management 35, no. 9 (2018): 2080–91. http://dx.doi.org/10.1108/ijqrm-01-2016-0001.

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Purpose Degraded failures and sudden critical failures are quite prevalent in industries. Degradation processes commonly belong to Weibull family and critical failures are found to follow exponential distribution. Therefore, it becomes important to carry out reliability and availability analysis of such systems. From the reported literature, it is learnt that models are available for the situations where the degraded failures as well as critical failures follow exponential distribution. The purpose of this paper is to present models suitable for reliability and availability analysis of systems

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Isupov, Konstantin, and Vladimir Knyazkov. "Multiple-precision matrix-vector multiplication on graphics processing units." Program Systems: Theory and Applications 11, no. 3 (2020): 61–84. http://dx.doi.org/10.25209/2079-3316-2020-11-3-61-84.

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We are considering a parallel implementation of matrix-vector multiplication (GEMV, Level 2 of the BLAS) for graphics processing units (GPUs) using multiple-precision arithmetic based on the residue number system. In our GEMV implementation, element-wise operations with multiple-precision vectors and matrices consist of several parts, each of which is calculated by a separate CUDA kernel. This feature eliminates branch divergence when performing sequential parts of multiple-precision operations and allows the full utilization of the GPU’s resources. An efficient data structure for storing arra

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Huang, Zhui Liang, Shu Wen Lin, and Dao Ying Jiang. "High-Precision Positioning and Speed Smooth Transition Control Algorithm for Terminal Point of Micro-Line Segment." Advanced Materials Research 305 (July 2011): 19–24. http://dx.doi.org/10.4028/www.scientific.net/amr.305.19.

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In allusion to the problem of data sampling interpolation error which exists in continuous micro-line segments interpolation algorithm with acceleration /deceleration control, this paper proposes a high-precision positioning and speed smooth transition control algorithm for terminal point of micro-line segment. The linear acceleration/deceleration mode was taken as an example to derive a motion control algorithm, which can eliminate the rounding error of the interpolation with fine adjusting the reserved parameters of acceleration /deceleration process when micro-line segment starting point an

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