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Journal articles on the topic 'A priori rounding error estimation'

Author: Grafiati

Published: 5 June 2025

Last updated: 15 July 2025

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1

Luther, Wolfram, and Werner Otten. "Reliable Computation of Elliptic Functions." JUCS - Journal of Universal Computer Science 4, no. (1) (1998): 25–33. https://doi.org/10.3217/jucs-004-01-0025.

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In this note we present rapidly convergent algorithms depending on the method of arithmetic-geometric means (AGM) for the computation of Jacobian elliptic functions and Jacobi's Theta-function. In particular, we derive explicit a priori bounds for the error accumulation of the corresponding Landen transform.

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2

Zhang, Haiyang, and Chenglin Wen. "A Higher-Order Extended Cubature Kalman Filter Method Using the Statistical Characteristics of the Rounding Error of the System Model." Mathematics 12, no. 8 (2024): 1168. http://dx.doi.org/10.3390/math12081168.

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The cubature Kalman filter (CKF) cannot accurately estimate the nonlinear model, and these errors will have an impact on the accuracy. In order to improve the filtering performance of the CKF, this paper proposes a new CKF method to improve the estimation accuracy by using the statistical characteristics of rounding error, establishes a higher-order extended cubature Kalman filter (RHCKF) for joint estimation of sigma sampling points and random variables of rounding error, and gives a solution method considering the rounding error of multi-level approximation of the original function in the un

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3

Ding, Linwang, and Chenglin Wen. "High-Order Extended Kalman Filter for State Estimation of Nonlinear Systems." Symmetry 16, no. 5 (2024): 617. http://dx.doi.org/10.3390/sym16050617.

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In general, the extended Kalman filter (EKF) has a wide range of applications, aiming to minimize symmetric loss function (mean square error) and improve the accuracy and efficiency of state estimation. As the nonlinear model complexity increases, rounding errors gradually amplify, leading to performance degradation. After multiple iterations, divergence may occur. The traditional extended Kalman filter cannot accurately estimate the nonlinear model, and these errors still have an impact on the accuracy. To improve the filtering performance of the extended Kalman filter (EKF), this paper propo

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4

Efird, Jimmy T. "Epidemiology of Rounding Error." Medicina 60, no. 12 (2024): 2105. https://doi.org/10.3390/medicina60122105.

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This work represents a significant contribution to understanding the importance of appropriately rounding numbers with minimal error. That is, to reduce inexact rounding and data truncation error and simultaneously eliminate unintentional misleading findings in epidemiological studies. The rounding of numbers represents a compromise solution that attempts to find a balance between the loss of information from reporting too few significant digits versus retaining more digits than necessary. Substituting a rounded number for its original value may be acceptable and practical in many applied situ

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5

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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6

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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7

Burr, T., M. S. Hamada, T. Cremers, et al. "Measurement error models and variance estimation in the presence of rounding error effects." Accreditation and Quality Assurance 16, no. 7 (2011): 347–59. http://dx.doi.org/10.1007/s00769-011-0791-0.

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8

Drzisga, Daniel, Brendan Keith, and Barbara Wohlmuth. "The Surrogate Matrix Methodology: A Priori Error Estimation." SIAM Journal on Scientific Computing 41, no. 6 (2019): A3806—A3838. http://dx.doi.org/10.1137/18m1226580.

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9

Sato, Yoshihiro, and Takuya Maruyama. "Modeling the Rounding of Departure Times in Travel Surveys: Comparing the Effect of Trip Purposes and Travel Modes." Transportation Research Record: Journal of the Transportation Research Board 2674, no. 10 (2020): 628–37. http://dx.doi.org/10.1177/0361198120935435.

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Rounding errors are often observed in reported trip departure and arrival times in paper-based travel surveys, and most of the reported times are multiples of 5, 15, 30, or 60 min. However, the rounding is rarely systematically analyzed. This study aimed to analyze the rounding of reported departure time in paper-based travel surveys by extending the rounding model proposed by Rietveld in 2002. The model parameters were estimated using the maximum likelihood method with constraints. The data in a 2012 household travel survey in Kumamoto, Japan, was used. The data in Japan were found to be ofte

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10

Rubio, Gonzalo, François Fraysse, David A. Kopriva, and Eusebio Valero. "Quasi-A Priori Truncation Error Estimation in the DGSEM." Journal of Scientific Computing 64, no. 2 (2014): 425–55. http://dx.doi.org/10.1007/s10915-014-9938-6.

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11

Wang, Xiang-Yu, Song Cen, C. F. Li, and D. R. J. Owen. "A priori error estimation for the stochastic perturbation method." Computer Methods in Applied Mechanics and Engineering 286 (April 2015): 1–21. http://dx.doi.org/10.1016/j.cma.2014.11.044.

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12

Ruge, P. "A priori local error estimation with adaptive time-stepping." Communications in Numerical Methods in Engineering 15, no. 7 (1999): 479–91. http://dx.doi.org/10.1002/(sici)1099-0887(199907)15:7<479::aid-cnm262>3.0.co;2-7.

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13

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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14

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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15

Dahleh, M., and M. Ricci. "On the SPR Condition in Output Error Estimation Schemes." Journal of Dynamic Systems, Measurement, and Control 115, no. 4 (1993): 704–8. http://dx.doi.org/10.1115/1.2899199.

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In this paper we will analyze the SPR condition in output error adaptive estimation schemes. An idea of Tomizuka is used to reduce the restrictive nature of the SPR condition, and is strengthened by exploiting certain a priori information on the uncertainty structure of the underlying plant, which is represented by an interval plant description. New results for the analysis of these types of systems are obtained, and are subsequently incorporated in the analysis of the adaptive system.

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16

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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17

Liang, Mingduan, Shuai Wen, and Ying Han. "Local Discontinuous Adaptive Finite Element Method for Steklov Eigenvalue Problems." Journal of Research in Applied Mathematics 11, no. 1 (2025): 55–73. https://doi.org/10.35629/0743-11015573.

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Using the flexibility of the finite element method to solve the solution problems on different shaped and natured elements, the local discontinuous Galerkin method can handle very complex boundary problems. Using the local discontinuous Galerkin method to perform a priori error estimation for the Steklov eigenvalue problem, we obtain a reasonable error estimation subspace, which can effectively solve the validity and reliability of the eigenfunction indicator subspace and the reliability of the eigenvalue error estimation indicator. We use precise numerical data obtained from MATLAB experiment

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18

Takeda, Takashi, and Toru Namerikawa. "A Sensor Network Configuration Considering Priori Estimation Error and Communication Energy." IFAC Proceedings Volumes 43, no. 8 (2010): 341–46. http://dx.doi.org/10.3182/20100712-3-fr-2020.00058.

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19

Prathap, Gangan. "A priori error estimation of finite element models from first principles." Sadhana 24, no. 3 (1999): 199–214. http://dx.doi.org/10.1007/bf02745801.

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20

Ritchie, Martin W. "Minimizing the Rounding Error from Point Sample Estimates of Tree Frequencies." Western Journal of Applied Forestry 12, no. 4 (1997): 108–14. http://dx.doi.org/10.1093/wjaf/12.4.108.

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Abstract Three solutions are presented for estimating stems per acre when trees are tallied by diameter class with horizontal point sampling. The first solution is based on the arithmetic mean of the diameter-class limits. The second is based on the geometric mean of the diameter-class limits and is unbiased for uniform within-class diameter distributions. The third is a harmonic mean solution; it is derived from the ratio of the geometric mean squared and the arithmetic mean. If the within-class distribution is linear, then the solution based on the geometric mean is preferable. Any of these

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21

Amairi, Messaoud. "Recursive set membership estimation for output–error fractional models with unknown–but–bounded errors." International Journal of Applied Mathematics and Computer Science 26, no. 3 (2016): 543–53. http://dx.doi.org/10.1515/amcs-2016-0038.

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Abstract This paper presents a new formulation for set-membership parameter estimation of fractional systems. In such a context, the error between the measured data and the output model is supposed to be unknown but bounded with a priori known bounds. The bounded error is specified over measurement noise, rather than over an equation error, which is mainly motivated by experimental considerations. The proposed approach is based on the optimal bounding ellipsoid algorithm for linear output-error fractional models. A numerical example is presented to show effectiveness and discuss results.

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22

Hossain, Muhammad Shakhawat, Chunguang Xiong, and Huafei Sun. "A priori and a posteriori error analysis of the first order hyperbolic equation by using DG method." PLOS ONE 18, no. 3 (2023): e0277126. http://dx.doi.org/10.1371/journal.pone.0277126.

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In this research article, a discontinuous Galerkin method with a weighted parameter θ and a penalty parameter γ is proposed for solving the first order hyperbolic equation. The key aim of this method is to design an error estimation for both a priori and a posteriori error analysis on general finite element meshes. It is also exposed to the reliability and effectiveness of both parameters in the order of convergence of the solutions. For a posteriori error estimation, residual adaptive mesh- refining algorithm is employed. A series of numerical experiments are illustrated that demonstrate the

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23

Hamdi, Saif Eddine, Messaoud Amairi, and Mohamed Aoun. "Recursive set-membership parameter estimation of fractional systems using orthotopic approach." Transactions of the Institute of Measurement and Control 40, no. 15 (2018): 4185–97. http://dx.doi.org/10.1177/0142331217744853.

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In this paper, set-membership parameter estimation of linear fractional-order systems is addressed for the case of unknown-but-bounded equation error. In such bounded-error context with a-priori known noise bounds, the main goal is to characterize the set of all feasible parameters. This characterization is performed using an orthotopic strategy adapted for fractional system parameter estimation. In the case of a fractional commensurate system, an iterative algorithm is proposed to deal with commensurate-order estimation. The performances of the proposed algorithm are illustrated by a numerica

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24

Liang, Zhenyu, Qin Jiang, Qingsong Liu, Luopeng Xu, and Fan Yang. "Fractional Landweber Regularization Method for Identifying the Source Term of the Time Fractional Diffusion-Wave Equation." Symmetry 17, no. 4 (2025): 554. https://doi.org/10.3390/sym17040554.

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In this paper, the inverse problem of identifying the source term of the time fractional diffusion-wave equation is studied. This problem is ill-posed, i.e., the solution (if it exists) does not depend on the measurable data. Under the priori bound condition, the condition stable result and the optimal error bound are all obtained. The fractional Landweber iterative regularization method is used to solve this inverse problem. Based on the priori regularization parameter selection rule and the posteriori regularization parameter selection rule, the error estimation between the regularization so

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25

Tamminen, J., E. Kyrölä, V. F. Sofieva, et al. "GOMOS data characterization and error estimation." Atmospheric Chemistry and Physics Discussions 10, no. 3 (2010): 6755–96. http://dx.doi.org/10.5194/acpd-10-6755-2010.

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Abstract. The Global Ozone Monitoring by Occultation of Stars (GOMOS) instrument uses stellar occultation technique for monitoring ozone and other trace gases in the stratosphere and mesosphere. The self-calibrating measurement principle of GOMOS together with a relatively simple data retrieval where only minimal use of a priori data is required, provides excellent possibilities for long term monitoring of atmospheric composition. GOMOS uses about 180 brightest stars as the light source. Depending on the individual spectral characteristics of the stars, the signal-to-noise ratio of GOMOS is ch

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26

Tamminen, J., E. Kyrölä, V. F. Sofieva, et al. "GOMOS data characterisation and error estimation." Atmospheric Chemistry and Physics 10, no. 19 (2010): 9505–19. http://dx.doi.org/10.5194/acp-10-9505-2010.

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Abstract. The Global Ozone Monitoring by Occultation of Stars (GOMOS) instrument uses stellar occultation technique for monitoring ozone, other trace gases and aerosols in the stratosphere and mesosphere. The self-calibrating measurement principle of GOMOS together with a relatively simple data retrieval where only minimal use of a priori data is required provides excellent possibilities for long-term monitoring of atmospheric composition. GOMOS uses about 180 of the brightest stars as its light source. Depending on the individual spectral characteristics of the stars, the signal-to-noise rati

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27

Kinoshita, Eisuke, Hideo Kosako, and Yoshiaki Kojima. "Automatic rounding error estimation and its applications. Solution of linear equations, Newton's and Mcauley's methods." Electronics and Communications in Japan (Part I: Communications) 69, no. 11 (1986): 11–20. http://dx.doi.org/10.1002/ecja.4410691102.

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28

Wang, Quanxiang, Tengjin Zhao, and Zhiyue Zhang. "Finite Volume Element Approximation for the Elliptic Equation with Distributed Control." International Journal of Differential Equations 2018 (November 1, 2018): 1–11. http://dx.doi.org/10.1155/2018/4753792.

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In this paper, we consider a priori error estimates for the finite volume element schemes of optimal control problems, which are governed by linear elliptic partial differential equation. The variational discretization approach is used to deal with the control. The error estimation shows that the combination of variational discretization and finite volume element formulation allows optimal convergence. Numerical results are provided to support our theoretical analysis.

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29

Li, Dewang, Meilan Qiu, and Zhongyi Ke. "Bayesian Estimation Analysis of Bernoulli Measurement Error Model for Longitudinal Data." International Journal of Applied Physics and Mathematics 10, no. 4 (2020): 160–66. http://dx.doi.org/10.17706/ijapm.2020.10.4.160-166.

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The Bayesian method is used to study the inference of the semi-parametric measurement error model (MEs) with longitudinal data. A semi-parametric Bayesian method combined with fracture prior and Gibbs sampling combined with Metropolis-Hastings (MH) algorithm is applied and applied to the simulation observation from the posterior distribution, and the combined Bayesian statistics of unknown parameters and measurement errors are obtained. We obtained Bayesian estimates of the parameters and covariates of the measurement error model. Under three different priori assumptions, four simulation studi

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30

Chang, Tao, Kazimierz Duzinkiewicz, and Mietek Brdys. "Bounding Approach to Parameter Estimation without Priori Knowledge on Model Structure Error." IFAC Proceedings Volumes 37, no. 11 (2004): 221–26. http://dx.doi.org/10.1016/s1474-6670(17)31616-6.

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31

Khoozan, Davood, and Bahar Firoozabadi. "A priori error estimation of upscaled coarse grids for water-flooding process." Canadian Journal of Chemical Engineering 94, no. 8 (2016): 1612–26. http://dx.doi.org/10.1002/cjce.22536.

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32

Xiaomin Cai, Xiaomin Cai, Shan Nie Shan Nie, and Qiuxia Tian Qiuxia Tian. "Mixed Finite Element Methods for Second-Order Elliptic Eigenvalue Problems." Journal of Research in Applied Mathematics 11, no. 3 (2025): 114–21. https://doi.org/10.35629/0743-1103114121.

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This paper focuses on the study of general elliptic eigenvalue problems and derives a priori error estimates for eigenvalues and eigenfunctions. First, based on the existence and uniqueness of solutions to the corresponding steady-state problem, a completely continuous operator 𝑇 is defined, and an abstract error estimation expression is derived through deduction. On this basis, further derivations yield error estimates for eigenvalues and 𝐿 2 -norm error estimates for eigenfunctions. Finally, the validity of the theoretical results is verified through numerical experiments on two-dimensional

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33

Le, Thang Duc. "HP estimation for the Cauchy problem for nonlinear elliptic equation." Science and Technology Development Journal - Natural Sciences 1, T5 (2018): 193–202. http://dx.doi.org/10.32508/stdjns.v1it5.553.

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In this paper, we investigate the Cauchy problem for a ND nonlinear elliptic equation in a bounded domain. As we know, the problem is severely ill-posed. We apply the Fourier truncation method to regularize the problem. Error estimates between the regularized solution and the exact solution are established in Hp space under some priori assumptions on the exact solution.

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34

Huang, Hao, Kun Zhao, Guifu Zhang, et al. "Quantitative Precipitation Estimation with Operational Polarimetric Radar Measurements in Southern China: A Differential Phase–Based Variational Approach." Journal of Atmospheric and Oceanic Technology 35, no. 6 (2018): 1253–71. http://dx.doi.org/10.1175/jtech-d-17-0142.1.

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AbstractQuantitative precipitation estimation (QPE) with polarimetric radar measurements suffers from different sources of uncertainty. The variational approach appears to be a promising way to optimize the radar QPE statistically. In this study a variational approach is developed to quantitatively estimate the rainfall rate (R) from the differential phase (ΦDP). A spline filter is utilized in the optimization procedures to eliminate the impact of the random errors in ΦDP, which can be a major source of error in the specific differential phase (KDP)-based QPE. In addition, R estimated from the

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35

Che, Haitao, Yiju Wang, and Zhaojie Zhou. "An Optimal Error Estimates ofH1-Galerkin Expanded Mixed Finite Element Methods for Nonlinear Viscoelasticity-Type Equation." Mathematical Problems in Engineering 2011 (2011): 1–18. http://dx.doi.org/10.1155/2011/570980.

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We investigate aH1-Galerkin mixed finite element method for nonlinear viscoelasticity equations based onH1-Galerkin method and expanded mixed element method. The existence and uniqueness of solutions to the numerical scheme are proved. A priori error estimation is derived for the unknown function, the gradient function, and the flux.

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36

Akylbayev, M. I., and I. E. Kaspirovich. "On some estimations of deviations between real solution and numerical solution of dynamical equations with regard for Baumgarte constraint stabilization." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 113, no. 1 (2024): 21–27. http://dx.doi.org/10.31489/2024m1/21-27.

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The numerical solution of a system of differential equations with constraints can be unstable due to the accumulation of rounding errors during the implementation of the difference scheme of numerical integration. To limit the amount of accumulation, the Baumgarte constraint stabilization method is used. In order to estimate the deviation of real solution from the numerical one the method of constraint stabilization can be used to derive required formulas. The well-known technique of expansion the deviation function to Taylor series is being used. The paper considers the estimation of the erro

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37

Lange, O., and B. Yang. "Optimization of array geometry for direction-of-arrival estimation using a priori information." Advances in Radio Science 8 (October 1, 2010): 87–94. http://dx.doi.org/10.5194/ars-8-87-2010.

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Abstract. This paper focuses on the estimation of the direction-of-arrival (DOA) of signals impinging on a sensor array. A novel method of array geometry optimization is presented that improves the DOA estimation performance compared to the standard uniform linear array (ULA) with half wavelength element spacing. Typically, array optimization only affects the beam pattern of a specific steering direction. In this work, the proposed objective function incorporates, on the one hand, a priori knowledge about the signal's DOA in terms of a probability density function. By this means, the array can

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38

Kolomys, O. M. "Estimation of the Rounding Error of the Algorithm for Calculating the Estimate of the Spectral Density." Mathematical and computer modelling. Series: Physical and mathematical sciences, no. 19 (June 25, 2019): 41–46. http://dx.doi.org/10.32626/2308-5878.2019-19.41-46.

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Moon, Kevin, Kumar Sricharan, Kristjan Greenewald, and Alfred Hero. "Ensemble Estimation of Information Divergence †." Entropy 20, no. 8 (2018): 560. http://dx.doi.org/10.3390/e20080560.

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Recent work has focused on the problem of nonparametric estimation of information divergence functionals between two continuous random variables. Many existing approaches require either restrictive assumptions about the density support set or difficult calculations at the support set boundary which must be known a priori. The mean squared error (MSE) convergence rate of a leave-one-out kernel density plug-in divergence functional estimator for general bounded density support sets is derived where knowledge of the support boundary, and therefore, the boundary correction is not required. The the

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Hu, Jun, Qiaoqiao Ge, Jihong Liu, Wenyan Yang, Zhigui Du, and Lehe He. "Constructing Adaptive Deformation Models for Estimating DEM Error in SBAS-InSAR Based on Hypothesis Testing." Remote Sensing 13, no. 10 (2021): 2006. http://dx.doi.org/10.3390/rs13102006.

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The Interferometric Synthetic Aperture Radar (InSAR) technique has been widely used to obtain the ground surface deformation of geohazards (e.g., mining subsidence and landslides). As one of the inherent errors in the interferometric phase, the digital elevation model (DEM) error is usually estimated with the help of an a priori deformation model. However, it is difficult to determine an a priori deformation model that can fit the deformation time series well, leading to possible bias in the estimation of DEM error and the deformation time series. In this paper, we propose a method that can co

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41

Liu, Yan, Hange Li, and Wei He. "Rotor Position Estimation Method for Permanent Magnet Synchronous Motor Based on High-Order Extended Kalman Filter." Electronics 13, no. 24 (2024): 4978. https://doi.org/10.3390/electronics13244978.

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To address the issue of decreased rotor position estimation accuracy in permanent magnet synchronous motors (PMSMs) caused by linearization rounding errors in the extended Kalman filter (EKF), this paper proposes a rotor position estimation method for PMSMs based on higher-order extended Kalman filtering. This method relies on the state-space equations of a PMSM in a stationary coordinate system and establishes a higher-order Taylor series expansion based on the least squares approach. It constructs a prediction and update model for the state variables using the higher-order Taylor series expa

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42

Pagani, Pietro, Riccardo Malpica Galassi, Ruggero Amaduzzi, Alessandro Parente, and Francesco Contino. "An enhanced Sample-Partitioning Adaptive Reduced Chemistry method with a-priori error estimation." Combustion and Flame 260 (February 2024): 113221. http://dx.doi.org/10.1016/j.combustflame.2023.113221.

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43

Tyrsin, A. N., and O. A. Golovanov. "Systems monitoring based on robust estimation of stochastic time series models." Journal of Physics: Conference Series 2388, no. 1 (2022): 012074. http://dx.doi.org/10.1088/1742-6596/2388/1/012074.

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Abstract The problem of system monitoring under conditions of stochastic data heterogeneity based on time series models is considered. The stability of monitoring is proposed to be ensured through the use of convex-concave loss functions. An algorithm for estimating the variance of the main error distribution is proposed. This allows using robust procedures for estimating the parameters of stochastic time series models without a priori information about the variance value of the main error distribution. Using the Monte Carlo statistical test method, the estimates of the proposed robust methods

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44

Kallinderis, Y., and C. Kontzialis. "A priori mesh quality estimation via direct relation between truncation error and mesh distortion." Journal of Computational Physics 228, no. 3 (2009): 881–902. http://dx.doi.org/10.1016/j.jcp.2008.10.023.

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45

Schneider, Patrick, and Reinhold Kienzler. "A priori estimation of the systematic error of consistently derived theories for thin structures." International Journal of Solids and Structures 190 (May 2020): 1–21. http://dx.doi.org/10.1016/j.ijsolstr.2019.10.010.

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46

Kim, Soo Min, Soo‐Won Chae, and Jin‐Gyun Kim. "Multiphysics model reduction of symmetric vibro‐acoustic formulation with a priori error estimation criteria." International Journal for Numerical Methods in Engineering 121, no. 23 (2020): 5381–404. http://dx.doi.org/10.1002/nme.6524.

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Galkin, P. S., and V. N. Lagutkin. "METHOD OF COMPENSATION OF IONOSPHERE ERRORS OF SPACE OBJECTS COORDINATES DEFINITION BY MEANS OF TWO POSITION RADAR OBSERVATION." Issues of radio electronics, no. 3 (March 20, 2018): 45–49. http://dx.doi.org/10.21778/2218-5453-2018-3-45-49.

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The algorithm of estimation and compensation of ionosphere influence on the measurement of parameters of the motion of space objects in two-position radar system with account of radio physical effects depending on elevation angles and the operating frequency is developed. It is assumed that the observed space object is traсked object, the orbital parameters which are well known, including the dependence of the velocity of the point on the orbit, and the uncertainty of the current coordinates of the object is caused mainly by forecast error of its position of in orbit (longitudinal error). To e

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Karaa, Samir. "A Priori Error Estimates for Mixed Finite Element Schemes for the Wave Equation." Sultan Qaboos University Journal for Science [SQUJS] 20, no. 2 (2015): 31. http://dx.doi.org/10.24200/squjs.vol20iss2pp31-41.

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A family of implicit-in-time mixed finite element schemes is presented for the numerical approximation of the acoustic wave equation. The mixed space discretization is based on the displacement form of the wave equation and the time-stepping method employs a three-level one-parameter scheme. A rigorous stability analysis is presented based on energy estimation and sharp stability results are obtained. A convergence analysis is carried out and optimal a priorierror estimates for both displacement and pressure are derived.

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Delaigle, Aurore. "Nonparametric kernel methods for curve estimation and measurement errors." Proceedings of the International Astronomical Union 10, S306 (2014): 28–39. http://dx.doi.org/10.1017/s1743921314013489.

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AbstractWe consider the problem of estimating an unknown density or regression curve from data. In the parametric setting, the curve to estimate is modelled by a function which is known up to the value of a finite number of parameters. We consider the nonparametric setting, where the curve is not modelled a priori. We focus on kernel methods, which are popular nonparametric techniques that can be used for both density and regression estimation. While these methods are appropriate when the data are observed accurately, they cannot be directly applied to astronomical data, which are often measur

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Reys, Robert E., Barbara J. Reys, Nobuhiko Nohda, Junichi Ishida, Shigeo Yoshikawa, and Katsuhiko Shimizu. "Computational Estimation Performance and Strategies used by Fifth- and Eighth-Grade Japanese Students." Journal for Research in Mathematics Education 22, no. 1 (1991): 39–58. http://dx.doi.org/10.5951/jresematheduc.22.1.0039.

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Four hundred and sixty-six fifth- and eighth-grade Japanese students were administered a computational estimation test. The fifth-grade mean was 7.39 and the eighth-grade mean was 11.15 on the 39-item open-ended test. Interviews with 21 students who had scored in the top 5% revealed that the Japanese students employed the three general cognitive processes outlined in a theoretical model based on interviews with United States students: reformulation, translation, and compensation. They also used many of the same strategies (front-end, compatible numbers, flexible rounding) utilized by American

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