Relevant bibliographies by topics / A priori rounding error estimation

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers
  5. Reports

Academic literature on the topic 'A priori rounding error estimation'

Author: Grafiati
Published: 5 June 2025
Last updated: 15 July 2025

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

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "A priori rounding error estimation"

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Riaz, Azba. "Une nouvelle formulation Galerkin discontinue pour équations de Maxwell en temps, a priori et a posteriori erreur estimation." Thesis, Cergy-Pontoise, 2016. http://www.theses.fr/2016CERG0790/document.

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Dans la première partie de cette thèse, nous avons considéré les équations de Maxwell en temps et construit une formulation discontinue de Galerkin (DG). On a montré que cette formulation est bien posée et ensuite on a établi des estimateurs a priori pour cette formulation. On a obtenu des résultats numériques pour valider les estimateurs a priori obtenus théoriquement. Dans la deuxième partie de cette thèse, des estimateurs d'erreur a posteriori de cette formulation sont établis, pour le cas semi-discret et pour le système complètement discrétisé. Dans la troisième partie de cette thèse, on c
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Jonsson, Tobias. "Cut finite element methods on parametric multipatch surfaces." Licentiate thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-159748.

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Salhi, Yamina. "Étude et réalisation de logiciels d'optimisation non contrainte avec dérivation numérique et estimation de la précision des résultats." Paris 6, 1985. http://www.theses.fr/1985PA066412.

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L'étude de ces logiciels est la suivante: sureté et rapidité de convergence, approximation de la matrice hersienne, contrôle de la propagation des erreurs d'arrondi et vectorisation sur cray-1 du code développé.
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Larsson, Karl. "Finite Element Methods for Thin Structures with Applications in Solid Mechanics." Doctoral thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-79297.

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Thin and slender structures are widely occurring both in nature and in human creations. Clever geometries of thin structures can produce strong constructions while requiring a minimal amount of material. Computer modeling and analysis of thin and slender structures have their own set of problems, stemming from assumptions made when deriving the governing equations. This thesis deals with the derivation of numerical methods suitable for approximating solutions to problems on thin geometries. It consists of an introduction and four papers. In the first paper we introduce a thread model for use i
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Cherfils, Laurence. "Méthode de cheminement adaptative pour les problèmes semi-linéaires dépendant d'un paramètre." Université Joseph Fourier (Grenoble), 1996. http://www.theses.fr/1996GRE10105.

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Ce travail consiste en l'élaboration d'une méthode de cheminement, dite également méthode de continuation, destinée aux problèmes de bifurcation qui apparaîssent lors de la discrétisation par éléments finis P1 d'une EDP semi-linéaire dépendant d'un paramètre. Afin de construire une méthode suffisamment robuste pour traiter les problèmes dont les solutions présentent des phénomènes de couches limites ou de singularités, nous avons intégré à la méthode de cheminement introduite par E. L. Allgower et K. Georg des techniques d'éléments finis adaptatifs, ainsi qu'une implémentation parallèle sur un
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Larsson, Karl. "Finite element methods for threads and plates with real-time applications." Licentiate thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-38198.

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Thin and slender structures are widely occurring both in nature and in human creations. Clever geometries of thin structures can produce strong constructions while using a minimal amount of material. Computer modeling and analysis of thin and slender structures has its own set of problems stemming from assumptions made when deriving the equations modeling their behavior from the theory of continuum mechanics. In this thesis we consider two kinds of thin elastic structures; threads and plates. Real-time simulation of threads are of interest in various types of virtual simulations such as surger
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(8800844), Jing Yang. "THE ERROR ESTIMATION IN FINITE ELEMENT METHODS FOR ELLIPTIC EQUATIONS WITH LOW REGULARITY." Thesis, 2020.

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<div> <div> <div> <p>This dissertation contains two parts: one part is about the error estimate for the finite element approximation to elliptic PDEs with discontinuous Dirichlet boundary data, the other is about the error estimate of the DG method for elliptic equations with low regularity. </p> <p>Elliptic problems with low regularities arise in many applications, error estimate for sufficiently smooth solutions have been thoroughly studied but few results have been obtained for elliptic problems with low regularities. Part I provides an error estimate for finite element approximation to ell
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Book chapters on the topic "A priori rounding error estimation"

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Iri, Masao, and Koichi Kubota. "Automatic Differentiation: Introduction, History, and Rounding Error Estimation." In Encyclopedia of Optimization. Springer Nature Switzerland, 2024. https://doi.org/10.1007/978-3-030-54621-2_26-1.

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Benner, Peter, and André Schneider. "Some Remarks on A Priori Error Estimation for ESVDMOR." In Scientific Computing in Electrical Engineering SCEE 2010. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22453-9_2.

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Braconnier, Thierry, and Philippe Langlois. "From Rounding Error Estimation to Automatic Correction with Automatic Differentiation." In Automatic Differentiation of Algorithms. Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4613-0075-5_42.

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Jézéquel, Fabienne, Stef Graillat, Daichi Mukunoki, Toshiyuki Imamura, and Roman Iakymchuk. "Can We Avoid Rounding-Error Estimation in HPC Codes and Still Get Trustworthy Results?" In Lecture Notes in Computer Science. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-63618-0_10.

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Mansouri, Majdi, Hazem Numan Nounou, and Mohamed Numan Nounou. "Modeling and Monitoring of Chemical System." In Handbook of Research on Modern Optimization Algorithms and Applications in Engineering and Economics. IGI Global, 2016. http://dx.doi.org/10.4018/978-1-4666-9644-0.ch032.

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This chapter addresses the problem of time-varying nonlinear modeling and monitoring of a continuously stirred tank reactor (CSTR) process using state estimation techniques. These techniques include the extended Kalman filter (EKF), particle filter (PF), and the more recently the variational Bayesian filter (VBF). The objectives of this chapter are threefold. The first objective is to use the variational Bayesian filter with better proposal distribution for nonlinear states and parameters estimation. The second objective is to extend the state and parameter estimation techniques to better handle nonlinear and non-Gaussian processes without a priori state information, by utilizing a time-varying assumption of statistical parameters. The third objective is to apply the state estimation techniques EKF, PF and VBF for time-varying nonlinear modeling and monitoring of CSTR process. The estimation performance is evaluated on a synthetic example in terms of estimation accuracy, root mean square error and execution times.
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Sohor, Andrii, and Markiian Sohor. "APPLICATION OF SVD METHOD IN SOLVING INCORRECT GEODESIC PROBLEMS." In Priority areas for development of scientific research: domestic and foreign experience. Publishing House “Baltija Publishing”, 2021. http://dx.doi.org/10.30525/978-9934-26-049-0-36.

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The most reliable method for calculating linear equations of the least squares principle, which can be used to solve incorrect geodetic problems, is based on matrix factorization, which is called a singular expansion. There are other methods that require less machine time and memory. But they are less effective in taking into account the errors of the source information, rounding errors and linear dependence. The methodology of such research is that for any matrix A and any two orthogonal matrices U and V there is a matrix Σ, which is determined from the ratio. The idea of a singular decomposition is that by choosing the right matrices U and V, you can convert most elements of the matrix to zero and make it diagonal with non-negative elements. The novelty and relevance of scientific solutions lies in the feasibility of using a singular decomposition of the matrix to obtain linear equations of the least squares method, which can be used to solve incorrect geodetic problems. The purpose of scientific research is to obtain a stable solution of parametric equations of corrections to the results of measurements in incorrect geodetic problems. Based on the performed research on the application of the singular decomposition method in solving incorrect geodetic problems, we can summarize the following. A singular expansion of a real matrix is any factorization of a matrix with orthogonal columns , an orthogonal matrix and a diagonal matrix , the elements of which are called singular numbers of the matrix , and the columns of matrices and left and right singular vectors. If the matrix has a full rank, then its solution will be unique and stable, which can be obtained by different methods. But the method of singular decomposition, in contrast to other methods, makes it possible to solve problems with incomplete rank. Research shows that the method of solving normal equations by sequential exclusion of unknowns (Gaussian method), which is quite common in geodesy, does not provide stable solutions for poorly conditioned or incorrect geodetic problems. Therefore, in the case of unstable systems of equations, it is proposed to use the method of singular matrix decomposition, which in computational mathematics is called SVD. The SVD singular decomposition method makes it possible to obtain stable solutions of both stable and unstable problems by nature. This possibility to solve incorrect geodetic problems is associated with the application of some limit τ, the choice of which can be made by the relative errors of the matrix of coefficients of parametric equations of corrections and the vector of results of geodetic measurements . Moreover, the solution of the system of normal equations obtained by the SVD method will have the shortest length. Thus, applying the apparatus of the singular decomposition of the matrix of coefficients of parametric equations of corrections to the results of geodetic measurements, we obtained new formulas for estimating the accuracy of the least squares method in solving incorrect geodetic problems. The derived formulas have a compact form and make it possible to easily calculate the elements and estimates of accuracy, almost ignoring the complex procedure of rotation of the matrix of coefficients of normal equations.
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Huxley, M. N. "Lattice points and area." In Area, Lattice Points, and Exponential Sums. Oxford University PressOxford, 1996. http://dx.doi.org/10.1093/oso/9780198534662.003.0019.

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Abstract The analytic method for estimating the discrepancy between the number of lattice points inside a closed curve involves dividing the curve into five or more pieces, taking local coordinates y =f(x) on each piece, and estimating the contribution ∑ p(f(m)) that each piece of the curve makes to the discrepancy. The classical estimate is Corollary 2 to Lemma 5.4.3. We use the Fourier expansion of Lemma 5.3.1, which leads to the sums considered in Chapter 8. Our first task is to use the estimates for the First Spacing Problem in Chapter 13 and the Second Spacing Problem in Chapter 16 to complete the estimation of the exponential sum, and deduce the bounds for the rounding error sum. As in the last section, we require that certain derivatives and determinants of derivatives do not vanish. We shall show that the local coordinate systems can be chosen to satisfy these conditions.
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O’Leary, Paul, and Matthew Harker. "Surface Modelling Using Discrete Basis Functions for Real-Time Automatic Inspection." In 3-D Surface Geometry and Reconstruction. IGI Global, 2012. http://dx.doi.org/10.4018/978-1-4666-0113-0.ch010.

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This chapter presents an introduction to discrete basis functions and their application to real-time automatic surface inspection. In particular, discrete polynomial basis functions are analyzed in detail. Emphasis is placed on a formal and stringent mathematical background, which enables an analytical a-priori estimation of the performance of the methods for specific applications. A generalized synthesis algorithm for discrete polynomial basis functions is presented. Additionally a completely new approach to synthesizing constrained basis functions is presented. The resulting constrained basis functions form a unitary matrix, i.e. are optimal with respect to numerical error propagation and have many applications, e.g. as admissible functions in Galerkin methods for to solution of boundary value and initial value problems. Furthermore, a number of case studies are presented, which show the applicability of the methods in real applications.
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Conference papers on the topic "A priori rounding error estimation"

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A., Takayasu, Oishi S., and Kubo T. "A Priori Inverse Operator Estimation for Guaranteed Error Estimate." In 4th International Workshop on Reliable Engineering Computing (REC 2010). Research Publishing Services, 2010. http://dx.doi.org/10.3850/978-981-08-5118-7_054.

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Marchuk, Vladimir, Sergey Makov, Dmitry Timofeev, Marina Pismenskova, and Alexandr Fisunov. "A method of signal estimation error reduction in a priori indeterminacy." In 2015 23rd Telecommunications Forum Telfor (TELFOR). IEEE, 2015. http://dx.doi.org/10.1109/telfor.2015.7377492.

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Abdallh, Ahmed Abou-Elyazied, Guillaume Crevecoeur, and Luc Dupre. "A priori error estimation of magnetic material characteristics using stochastic uncertainty analysis." In 2010 14th Biennial IEEE Conference on Electromagnetic Field Computation (CEFC 2010). IEEE, 2010. http://dx.doi.org/10.1109/cefc.2010.5481288.

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"A HYBRID APPROACH FOR HIGH QUALITY REAL-TIME TERRAIN RENDERING AND OPTIMIZED A-PRIORI ERROR ESTIMATION." In International Conference on Computer Graphics Theory and Applications. SciTePress - Science and and Technology Publications, 2010. http://dx.doi.org/10.5220/0002824602330238.

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Rainsberger, Robert B., Jeffrey T. Fong, and Pedro V. Marcal. "Application of an a priori Jacobian-Based Error Estimation Metric to the Accuracy Assessment of 3D Finite Element Simulations." In ASME 2018 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/pvp2018-84784.

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The determinant of the Jacobian matrix is frequently used in the Finite Element Method as a measure of mesh quality. A new metric is defined, called the Standard Error, based on the distribution of the determinants of the Jacobian matrices of all elements of a finite element mesh. Where the Jacobian norm can be used to compare the quality of one element to another of the same type, the Standard Error compares the mesh quality of different versions of a finite element model where each version uses a different element type. To motivate this new Standard Error, we investigate the geometric meanin
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Volponi, Allan J. "Sensor Error Compensation in Engine Performance Diagnostics." In ASME 1994 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/94-gt-058.

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The pursuit of reliable engine performance methods is as old as the gas turbine itself. Contemporary methods of engine fault isolation and assessment have centered around the use of modem estimation algorithms similar in nature to the Kalman filter and its derivatives. Those who are familar with such programs will offer the following quip, (apparently known to many but attributed to none), that the Kalman filter works well when you already know the answer, in other words, when the a-priori estimates are sufficiently close to the true values such as to produce small measurement residuals. Unfor
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Lewander, Magnus, Per Tunesta˚l, and Bengt Johansson. "Cylinder Individual Efficiency Estimation for Online Fuel Consumption Optimization." In ASME 2010 Internal Combustion Engine Division Fall Technical Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/icef2010-35113.

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Engine efficiency is often controlled in an indirect way through combustion timing control. This requires a priori knowledge of where to phase the combustion for different operating points and conditions. With cylinder individual efficiency estimation, control strategies aiming directly at fuel consumption optimization can be developed. This paper presents a method to estimate indicated efficiency using the cylinder pressure trace as input. The proposed method is based on a heat release calculation that takes heat losses into account implicitly using an estimated, CAD resolved polytropic expon
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Niles, Kenneth, Steven Bunkley, W. Jacob Wagner, Isaac Blankenau, Anton Netchaev, and Ahmet Soylemezoglu. "SATELLITE IMAGE TEMPLATE MATCHING WITH COVARIANCE ESTIMATION FOR UNMANNED GROUND VEHICLE LOCALIZATION: ACTIVE TERRAIN LOCALIZATION IMAGING SYSTEM (ATLIS)." In 2024 NDIA Michigan Chapter Ground Vehicle Systems Engineering and Technology Symposium. National Defense Industrial Association, 2024. http://dx.doi.org/10.4271/2024-01-3995.

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&lt;title&gt;ABSTRACT&lt;/title&gt; &lt;p&gt;Robotic platforms require accurate geo-spatial localization for high-level mission planning, real-time site reconnaissance, and multi-machine collaboration. Global navigation satellite system (GNSS) receivers are most commonly used to provide UGVs with accurate geolocation. However, GNSS is not reliable in contested environments because it is vulnerable to jamming, spoofing and black-outs. To address these issues, the United States Army Corps of Engineers (USACE) -Engineer Research and Development Center (ERDC) has developed the Active Terrain Local
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Winstroth, Jan, and Joerg R. Seume. "Error Assessment of Blade Deformation Measurements on a Multi-Megawatt Wind Turbine Based on Digital Image Correlation." In ASME Turbo Expo 2015: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/gt2015-43622.

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Optical full-field measurement methods such as Digital Image Correlation (DIC) provide a new opportunity for measuring deformation and vibration in wind turbine rotor blades during operation, in high spatial and temporal resolution. Recent field tests on a multi-megawatt wind turbine have demonstrated the vast potential for full scale testing, however little is known about the overall accuracy of DIC measurements on wind turbines. The present work proposes using a virtual 3D wind turbine model for estimating the error associated with the optical measurements. The entire setup is simulated a pr
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Cossart, Q., F. Colas, and X. Kestelyn. "A priori error estimation of the structure-preserving modal model reduction by state residualization of a grid forming converter for use in 100% power electronics transmission systems." In 15th IET International Conference on AC and DC Power Transmission (ACDC 2019). Institution of Engineering and Technology, 2019. http://dx.doi.org/10.1049/cp.2019.0067.

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Reports on the topic "A priori rounding error estimation"

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Shkurupiy, Valeria, and Nikita Budnyi. A priori estimation of instrumental error of energy characteristics of an electric rocket engine. Baltic State Technical University “VOENMEH” named after D.F.Ustinov, 2023. http://dx.doi.org/10.12731/edn:dkwobv.

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In this work, the power of the calculated electric rocket engine (ERE) requires thrust, specific impulse, and efficiency. ERE thrust measurement is interesting enough to achieve smallness of rapid growth. Specific impulse and efficiency are measured using laboratory methods. For this reason, one should naturally approach the choice of design parameters and the composition of the measuring system. One of the synthesis products can be the minimization of measurement errors. The paper approaches an approach to a priori instrumental estimation of the error determination, which may be useful in the
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