Relevant bibliographies by topics / Numerical error

Contents

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

Academic literature on the topic 'Numerical error'

Author: Grafiati
Published: 4 June 2021
Last updated: 7 December 2024

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Journal articles on the topic "Numerical error"

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Duyan, Yalçın Akın, and Fuat Balcı. "Numerical error monitoring." Psychonomic Bulletin & Review 25, no. 4 (2018): 1549–55. http://dx.doi.org/10.3758/s13423-018-1506-x.

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La Follette, Peter T., Adriaan J. Teuling, Nans Addor, Martyn Clark, Koen Jansen, and Lieke A. Melsen. "Numerical daemons of hydrological models are summoned by extreme precipitation." Hydrology and Earth System Sciences 25, no. 10 (2021): 5425–46. http://dx.doi.org/10.5194/hess-25-5425-2021.

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Abstract. Hydrological models are usually systems of nonlinear differential equations for which no analytical solutions exist and thus rely on numerical solutions. While some studies have investigated the relationship between numerical method choice and model error, the extent to which extreme precipitation such as that observed during hurricanes Harvey and Katrina impacts numerical error of hydrological models is still unknown. This knowledge is relevant in light of climate change, where many regions will likely experience more intense precipitation. In this experiment, a large number of hydrographs are generated with the modular modeling framework FUSE (Framework for Understanding Structural Errors), using eight numerical techniques across a variety of forcing data sets. All constructed models are conceptual and lumped. Multiple model structures, parameter sets, and initial conditions are incorporated for generality. The computational cost and numerical error associated with each hydrograph were recorded. Numerical error is assessed via root mean square error and normalized root mean square error. It was found that the root mean square error usually increases with precipitation intensity and decreases with event duration. Some numerical methods constrain errors much more effectively than others, sometimes by many orders of magnitude. Of the tested numerical methods, a second-order adaptive explicit method is found to be the most efficient because it has both a small numerical error and a low computational cost. A small literature review indicates that many popular modeling codes use numerical techniques that were suggested by this experiment to be suboptimal. We conclude that relatively large numerical errors may be common in current models, highlighting the need for robust numerical techniques, in particular in the face of increasing precipitation extremes.
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Tzeng, Jengnan. "Linear Regression to Minimize the Total Error of the Numerical Differentiation." East Asian Journal on Applied Mathematics 7, no. 4 (2017): 810–26. http://dx.doi.org/10.4208/eajam.161016.300517a.

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AbstractIt is well known that numerical derivative contains two types of errors. One is truncation error and the other is rounding error. By evaluating variables with rounding error, together with step size and the unknown coefficient of the truncation error, the total error can be determined. We also know that the step size affects the truncation error very much, especially when the step size is large. On the other hand, rounding error will dominate numerical error when the step size is too small. Thus, to choose a suitable step size is an important task in computing the numerical differentiation. If we want to reach an accuracy result of the numerical difference, we had better estimate the best step size. We can use Taylor Expression to analyze the order of truncation error, which is usually expressed by the big O notation, that is, E(h) = Chk. Since the leading coefficient C contains the factor f(k)(ζ) for high order k and unknown ζ, the truncation error is often estimated by a roughly upper bound. If we try to estimate the high order difference f(k)(ζ), this term usually contains larger error. Hence, the uncertainty of ζ and the rounding errors hinder a possible accurate numerical derivative.We will introduce the statistical process into the traditional numerical difference. The new method estimates truncation error and rounding error at the same time for a given step size. When we estimate these two types of error successfully, we can reach much better modified results. We also propose a genetic approach to reach a confident numerical derivative.
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Cviklovič, V., D. Hrubý, M. Olejár, and O. Lukáč. "Comparison of numerical integration methods in strapdown inertial navigation algorithm  ." Research in Agricultural Engineering 57, Special Issue (2011): S30—S34. http://dx.doi.org/10.17221/58/2010-rae.

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The numerical mathematical theory provides a few ways of numerical integration with different errors. It is necessary to make use of the most exact method with respect to the computing power for a majority of microprocessors, because errors are integrated within them due to the algorithm. In our contribution, trapezoidal rule and Romberg’s method of numerical integration are compared in the velocity calculation algorithm of the strapdown inertial navigation. The sample frequency of acceleration and angular velocity measurement was 816.6599 Hz. Inertial navigation velocity was compared with precise incremental encoder data. Trapezoidal method velocity error in this example was 1.23 × 10<sup>–3</sup> m/s in the fifteenth-second measurement. Romberg’s method velocity error was 0.16 × 10<sup>–3 </sup>m/s for the same input data. The numerical mathematical theory provides a few ways of numerical integration with different errors. It is necessary to make use of the most exact method with respect to the computing power for a majority of microprocessors, because errors are integrated within them due to the algorithm. In our contribution, trapezoidal rule and Romberg’s method of numerical integration are compared in the velocity calculation algorithm of the strapdown inertial navigation. The sample frequency of acceleration and angular velocity measurement was 816.6599 Hz. Inertial navigation velocity was compared with precise incremental encoder data. Trapezoidal method velocity error in this example was 1.23 × 10<sup>–3</sup> m/s in the fifteenth-second measurement. Romberg’s method velocity error was 0.16 × 10<sup>–3 </sup>m/s for the same input data.
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Cui, Jing Jun. "Analysis of Machining Error in Numerical Control Milling." Applied Mechanics and Materials 312 (February 2013): 710–13. http://dx.doi.org/10.4028/www.scientific.net/amm.312.710.

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Generally speaking, the error in machining is an important indicator measuring the accuracy of finished surface. The machining error often occurs in numerical control milling. Such error will be influenced by multiple factors, such as cutter wear, thermal deformation, machine tool deformation, vibration or positioning error. Nowadays, though our science and technology develops rapidly, machining error problem in numerical control milling occurs frequently. At present, several methods can be applied to forecast machining error problems in numerical control milling, including on the basis of machining theory, experimental study, design study and artificial intelligence. The analysis and forecast of machining error problems in numerical control milling can to some extent improve the degree of machining errors so as to promote the machining accuracy in milling. The author expresses the views on machining error problems according to current situations of numerical control milling.
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Ferreira, F., E. Gendron, G. Rousset, and D. Gratadour. "Numerical estimation of wavefront error breakdown in adaptive optics." Astronomy & Astrophysics 616 (August 2018): A102. http://dx.doi.org/10.1051/0004-6361/201832579.

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Aims. Adaptive optics (AO) system performance is improved using post-processing techniques, such as point spread function (PSF) deconvolution. The PSF estimation involves characterization of the different wavefront (WF) error sources in the AO system. We propose a numerical error breakdown estimation tool that allows studying AO error source behavior such as their correlations. We also propose a new analytical model for anisoplanatism and bandwidth errors that were validated with the error breakdown estimation tool. This model is the first step for a complete AO residual error model that is expressed in deformable mirror space, leading to practical usage such as PSF reconstruction or turbulent parameters identification. Methods. We have developed in the computing platform for adaptive optics systems (COMPASS) code, which is an end-to-end simulation code using graphics processing units (GPU) acceleration, an estimation tool that provides a comprehensive error breakdown by the outputs of a single simulation run. We derive the various contributors from the end-to-end simulator at each iteration step: this method provides temporal buffers of each contributor. Then, we use this tool to validate a new model of anisoplanatism and bandwidth errors including their correlation. This model is based on a statistical approach that computes the error covariance matrices using structure functions. Results. On a SPHERE-like system, the comparison between a PSF computed from the error breakdown with a PSF obtained from classical end-to-end simulation shows that the statistics convergence limits converge very well, with a sub-percent difference in terms of Strehl ratio and ensquared energy at 5λ/D separation. A correlation analysis shows significant correlations between some contributors, especially WF measurement deviation error and bandwidth error due to centroid gain, and the well-known correlation between bandwidth and anisoplanatism errors is also retrieved. The model we propose for the two latter errors shows an SR and EE difference of about one percent compared to the end-to-end simulation, even if some approximations exist.
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T., V., Solomon G. Mikhlin, and Reinhard Lehmann. "Error Analysis in Numerical Processes." Mathematics of Computation 60, no. 201 (1993): 431. http://dx.doi.org/10.2307/2153180.

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Kinsella, A. "Numerical methods for error evaluation." American Journal of Physics 54, no. 5 (1986): 464–66. http://dx.doi.org/10.1119/1.14588.

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Stollberger, Claudia. "Correction: Numerical Error in Abstract." Annals of Internal Medicine 120, no. 4 (1994): 347. http://dx.doi.org/10.7326/0003-4819-120-4-199402150-00031.

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Huang, Yu Bin, Wei Sun, Qing Chao Sun, Yue Ma, and Hong Fu Wang. "Numerical Analysis of Thermal Error for a 4-Axises Horizontal Machining Center." Applied Mechanics and Materials 868 (July 2017): 64–68. http://dx.doi.org/10.4028/www.scientific.net/amm.868.64.

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Thermal deformations of machine tool are among the most significant error source of machining errors. Most of current thermal error modeling researches is about 3-axies machine tool, highly reliant on collected date, which could not predict thermal errors in design stage. In This paper, in order to estimate the thermal error of a 4-axise horizontal machining center. A thermal error prediction method in machine tool design stage is proposed. Thermal errors in workspace in different working condition are illustrated through numerical simulation and volumetric error model. Verification experiments shows the outcomes of this prediction method are basically correct.
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Dissertations / Theses on the topic "Numerical error"

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Jenkins, Siân. "Numerical model error in data assimilation." Thesis, University of Bath, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.665395.

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In this thesis, we produce a rigorous and quantitative analysis of the errors introduced by finite difference schemes into strong constraint 4D-Variational (4D-Var) data assimilation. Strong constraint 4D-Var data assimilation is a method that solves a particular kind of inverse problem; given a set of observations and a numerical model for a physical system together with a priori information on the initial condition, estimate an improved initial condition for the numerical model, known as the analysis vector. This method has many forms of error affecting the accuracy of the analysis vector, and is derived under the assumption that the numerical model is perfect, when in reality this is not true. Therefore it is important to assess whether this assumption is realistic and if not, how the method should be modified to account for model error. Here we analyse how the errors introduced by finite difference schemes used as the numerical model, affect the accuracy of the analysis vector. Initially the 1D linear advection equation is considered as our physical system. All forms of error, other than those introduced by finite difference schemes, are initially removed. The error introduced by `representative schemes' is considered in terms of numerical dissipation and numerical dispersion. A spectral approach is successfully implemented to analyse the impact on the analysis vector, examining the effects on unresolvable wavenumber components and the l2-norm of the error. Subsequently, a similar also successful analysis is conducted when observation errors are re-introduced to the problem. We then explore how the results can be extended to weak constraint 4D-Var. The 2D linear advection equation is then considered as our physical system, demonstrating how the results from the 1D problem extend to 2D. The linearised shallow water equations extend the problem further, highlighting the difficulties associated with analysing a coupled system of PDEs.
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Reddinger, Kaitlin Sue. "Numerical Stability & Numerical Smoothness of Ordinary Differential Equations." Bowling Green State University / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1431597407.

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Tomita, Yu. "Numerical and analytical studies of quantum error correction." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/53468.

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A reliable large-scale quantum computer, if built, can solve many real-life problems exponentially faster than the existing digital devices. The biggest obstacle to building one is that they are extremely sensitive and error-prone regardless of the selection of physical implementation. Both data storage and data manipulation require careful implementation and precise control due to its quantum mechanical nature. For the development of a practical and scalable computer, it is essential to identify possible quantum errors and reduce them throughout every layer of the hierarchy of quantum computation. In this dissertation, we present our investigation into new methods to reduce errors in quantum computers from three different directions: quantum memory, quantum control, and quantum error correcting codes. For quantum memory, we pursue the potential of the quantum equivalent of a magnetic hard drive using two-body-interaction structures in fractal dimensions. With regard to quantum control, we show that it is possible to arbitrarily reduce error when manipulating multiple quantum bits using a technique popular in nuclear magnetic resonance. Finally, we introduce an efficient tool to study quantum error correcting codes and present analysis of the codes' performance on model quantum architectures.
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Romutis, Todd. "Numerical Smoothness and Error Analysis for Parabolic Equations." Bowling Green State University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1522150799203255.

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Harlim, John. "Errors in the initial conditions for numerical weather prediction a study of error growth patterns and error reduction with ensemble filtering /." College Park, Md. : University of Maryland, 2006. http://hdl.handle.net/1903/3430.

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Thesis (Ph. D.) -- University of Maryland, College Park, 2006.<br>Thesis research directed by: Applied Mathematics and Scientific Computation Program. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Pinchuk, Amy Ruth. "Automatic adaptive finite element mesh generation and error estimation." Thesis, McGill University, 1985. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=63269.

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Küther, Marc. "Error estimates for numerical approximations to scalar conservation laws." [S.l. : s.n.], 2001. http://www.freidok.uni-freiburg.de/volltexte/337.

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Ndamase-, Nzuzo Pumla Patricia. "Numerical error analysis in foundation phase (Grade 3) mathematics." Thesis, University of Fort Hare, 2014. http://hdl.handle.net/10353/5893.

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The focus of the research was on numerical errors committed in foundation phase mathematics. It therefore explored: (1) numerical errors learners in foundation phase mathematics encounter (2) relationships underlying numerical errors and (3) the implementable strategies suitable for understanding numerical error analysis in foundation phase mathematics (Grade 3). From 375 learners who formed the population of the study in the primary schools (16 in total), the researcher selected by means of a simple random sample technique 80 learners as the sample size, which constituted 10% of the population as response rate. On the basis of the research questions and informed by positivist paradigm, a quantitative approach was used by means of tables, graphs and percentages to address the research questions. A Likert scale was used with four categories of responses ranging from (A) Agree, (S A) Strongly Agree, (D) Disagree and (S D) Strongly Disagree. The results revealed that: (1) the underlying numerical errors that learners encounter, include the inability to count backwards and forwards, number sequencing, mathematical signs, problem solving and word sums (2) there was a relationship between committing errors and a) copying numbers b) confusion of mathematical signs or operational signs c) reading numbers which contained more than one digit (3) It was also revealed that teachers needed frequent professional training for development; topics need to change and lastly government needs to involve teachers at ground roots level prior to policy changes on how to implement strategies with regards to numerical errors in the foundational phase. It is recommended that attention be paid to the use of language and word sums in order to improve cognition processes in foundation phase mathematics. Moreover, it recommends that learners are to be assisted time and again when reading or copying their work, so that they could have fewer errors in foundation phase mathematics. Additionally it recommends that teachers be trained on how to implement strategies of numerical error analysis in foundation phase mathematics. Furthermore, teachers can use tests to identify learners who could be at risk of developing mathematical difficulties in the foundation phase.
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Higham, D. J. "Error control in nonstiff initial value solvers." Thesis, University of Manchester, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.234210.

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Wyant, Timothy Joseph. "Numerical study of error propagation in Monte Carlo depletion simulations." Thesis, Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/44809.

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Improving computer technology and the desire to more accurately model the heterogeneity of the nuclear reactor environment have made the use of Monte Carlo depletion codes more attractive in recent years, and feasible (if not practical) even for 3-D depletion simulation. However, in this case statistical uncertainty is combined with error propagating through the calculation from previous steps. In an effort to understand this error propagation, four test problems were developed to test error propagation in the fuel assembly and core domains. Three test cases modeled and tracked individual fuel pins in four 17x17 PWR fuel assemblies. A fourth problem modeled a well-characterized 330MWe nuclear reactor core. By changing the code's initial random number seed, the data produced by a series of 19 replica runs of each test case was used to investigate the true and apparent variance in k-eff, pin powers, and number densities of several isotopes. While this study does not intend to develop a predictive model for error propagation, it is hoped that its results can help to identify some common regularities in the behavior of uncertainty in several key parameters.
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Books on the topic "Numerical error"

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L, Chiappetta, Gosman A. D, and United States. National Aeronautics and Space Administration., eds. Error reduction program: Final report. National Aeronautics and Space Administration, 1985.

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Thomas, Nehrkorn, Grassotti Christopher, and United States. National Aeronautics and Space Administration., eds. Distortion representation of forecast errors for model skill assessment and objective analysis: Technical report. National Aeronautics and Space Administration, 1997.

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1961-, Hammer R., ed. Numerical toolbox for verified computing. Springer-Verlag, 1993.

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Lin, Shu. On codes with multi-level error-correction capabilities. National Aeronautics and Space Administration, 1987.

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Shu, Lin. On codes with multi-level error-correction capabilities. National Aeronautics and Space Administration, 1987.

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Novak, Erich. Deterministic and Stochastic Error Bounds in Numerical Analysis. Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0079792.

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Novak, Erich. Deterministic and stochastic error bounds in numerical analysis. Springer-Verlag, 1988.

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G, Kalit, and Ames Research Center, eds. Mean-square error bounds for reduced-order linear state estimators. National Aeronautics and Space Administration, Ames Research Center, 1987.

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G, Kalit, and Ames Research Center, eds. Mean-square error bounds for reduced-order linear state estimators. National Aeronautics and Space Administration, Ames Research Center, 1987.

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Baram, Yoram. Mean-square error bounds for reduced-order linear state estimators. National Aeronautics and Space Administration, Ames Research Center, 1987.

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Book chapters on the topic "Numerical error"

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Hromadka, Theodore V., and Robert J. Whitley. "Numerical Error Analysis." In Advances in the Complex Variable Boundary Element Method. Springer London, 1998. http://dx.doi.org/10.1007/978-1-4471-3611-8_5.

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Stoer, J., and R. Bulirsch. "Error Analysis." In Introduction to Numerical Analysis. Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4757-2272-7_1.

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Stoer, J., and R. Bulirsch. "Error Analysis." In Introduction to Numerical Analysis. Springer New York, 2002. http://dx.doi.org/10.1007/978-0-387-21738-3_1.

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Rüter, Marcus Olavi. "Numerical Integration." In Error Estimates for Advanced Galerkin Methods. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-06173-9_5.

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Rüter, Marcus Olavi. "Numerical Examples." In Error Estimates for Advanced Galerkin Methods. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-06173-9_9.

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Antia, H. M. "Roundoff Error." In Numerical Methods for Scientists and Engineers. Hindustan Book Agency, 2012. http://dx.doi.org/10.1007/978-93-86279-52-1_2.

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Brass, H. "Error Bounds Based on Approximation Theory." In Numerical Integration. Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2646-5_12.

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Allahviranloo, Tofigh, Witold Pedrycz, and Armin Esfandiari. "Error Analysis." In Advances in Numerical Analysis Emphasizing Interval Data. CRC Press, 2021. http://dx.doi.org/10.1201/9781003218173-2.

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Köhler, Peter. "Intermediate Error Estimates for Quadrature Formulas." In Numerical Integration IV. Birkhäuser Basel, 1993. http://dx.doi.org/10.1007/978-3-0348-6338-4_16.

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Mastroianni, Giuseppe, and Péter Vértesi. "Error Estimates of Product Quadrature Formulae." In Numerical Integration IV. Birkhäuser Basel, 1993. http://dx.doi.org/10.1007/978-3-0348-6338-4_19.

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Conference papers on the topic "Numerical error"

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Radler, Simon, and Manfred Hajek. "Periodic Free Wake Simulation Using a Numerical Optimization Method." In Vertical Flight Society 72nd Annual Forum & Technology Display. The Vertical Flight Society, 2016. http://dx.doi.org/10.4050/f-0072-2016-11373.

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A novel method has been developed for the free vortex wake simulation of rotors under the assumption of periodicity. An error measure is introduced which is based on the mismatch between prevailing convection velocities and the assumed wake element positions. The systematic reduction of this defined error results in a numerically robust method for the computation of wake geometries. Two strategies are compared for the error reduction. The first uses the repeated evaluation of the velocity field to update the wake geometry as long as the defined error decreases. In the second strategy, the application of a Levenberg-Marquardt method is added, in which the error is further reduced using an analytically defined Jacobian matrix. Results correlate well with experiments for single rotor and tandem rotor cases. While the Levenberg-Marquardt method achieves an additional error reduction, correlation with experimental data is not generally improved by including this method.
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Demeure, Nestor, Cedric Chevalier, Christophe Denis, and Pierre Dossantos-Uzarralde. "Tagged error: tracing numerical error through computations." In 2021 IEEE 28th Symposium on Computer Arithmetic (ARITH). IEEE, 2021. http://dx.doi.org/10.1109/arith51176.2021.00014.

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Gustafson, John. "The end of numerical error." In 2015 IEEE 22nd Symposium on Computer Arithmetic (ARITH). IEEE, 2015. http://dx.doi.org/10.1109/arith.2015.34.

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Pötzelberger, Klaus. "Consistency of the empirical quantization error." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756158.

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Alefeld, G. "Complementarity Problems: Error Bounds for Approximate Solutions." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2990973.

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Butler, Brian K., and Paul H. Siegel. "Numerical issues affecting LDPC error floors." In GLOBECOM 2012 - 2012 IEEE Global Communications Conference. IEEE, 2012. http://dx.doi.org/10.1109/glocom.2012.6503607.

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Hladík, Milan, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Error Bounds on the Spectral Radius of Uncertain Matrices." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636875.

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Hollevoet, D., M. Van Daele, and G. Vanden Berghe. "On the Leading Error Term of Exponentially Fitted Numerov Methods." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2991074.

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Fu, Zhoulai, Zhaojun Bai, and Zhendong Su. "Automated backward error analysis for numerical code." In SPLASH '15: Conference on Systems, Programming, Languages, and Applications: Software for Humanity. ACM, 2015. http://dx.doi.org/10.1145/2814270.2814317.

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Der, Gim, and Roy Danchick. "Analytic and numerical error covariance matrix propagation." In Astrodynamics Conference. American Institute of Aeronautics and Astronautics, 1996. http://dx.doi.org/10.2514/6.1996-3661.

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Reports on the topic "Numerical error"

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Jameson, L. Numerical Errors in DNS: Total Run-Time Error. Office of Scientific and Technical Information (OSTI), 2000. http://dx.doi.org/10.2172/793863.

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Babuska, I., T. Strouboulis, C. S. Upadhyay, S. K. Gangaraj, and K. Copps. Validation of A-Posteriori Error Estimators by Numerical Approach. Defense Technical Information Center, 1993. http://dx.doi.org/10.21236/ada269493.

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Zoller, Miklos. Error Analysis on Numerical Integration Algorithms in a Hypoelasticity Framework. Office of Scientific and Technical Information (OSTI), 2021. http://dx.doi.org/10.2172/1806423.

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Radtke, Gregg Arthur, Keith L. Cartwright, and Lawrence C. Musson. Stochastic Richardson Extrapolation Based Numerical Error Estimation for Kinetic Plasma Simulations. Office of Scientific and Technical Information (OSTI), 2015. http://dx.doi.org/10.2172/1504853.

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Parker, S. E., and C. K. Birdsall. Numerical error in electron orbits with large. omega. sub ce. delta. t. Office of Scientific and Technical Information (OSTI), 1989. http://dx.doi.org/10.2172/6055858.

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Jameson, L. Direct Numerical Simulation DNS: Maximum Error as a Function of Mode Number. Office of Scientific and Technical Information (OSTI), 2000. http://dx.doi.org/10.2172/793962.

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Reasor, Jr, Bhamidipati Daniel A., Woolf Keerti K., and Reagan K. Numerical Predictions of Static-Pressure-Error Corrections for a Modified T-38C Aircraft. Defense Technical Information Center, 2014. http://dx.doi.org/10.21236/ada614715.

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8

Torres, Marissa, Michael-Angelo Lam, Levi Cass, Matt Malej, and Fengyan Shi. Getting started with FUNWAVE-TVD : troubleshooting guidance and recommendations. Engineer Research and Development Center (U.S.), 2024. http://dx.doi.org/10.21079/11681/48631.

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This technical note reviews some common initialization errors when first getting started with the numerical wave model, FUNWAVE-TVD (Fully Nonlinear Wave model–Total Variation Diminishing), and provides guidance for correcting these errors. Recommendations for troubleshooting the source or cause of instabilities in an application of the model as well as recognizing the difference between physical and numerical instabilities are also outlined and discussed. In addition, a quick start troubleshooting guide is provided in the Appendix. This guidance is particularly useful for novice to intermediate users of FUNWAVE-TVD who are less familiar with the workflow of setting up the model and interpreting error output statements. From this document, users will gain a fundamental understanding of practical troubleshooting techniques for FUNWAVE-TVD that will improve the problem-solving workflow and enhance the final product of a wave modeling study. Providing coastal planners and engineers with ease of model access and usability guidance facilitates efficient screening of design alternatives for effective decision-making under environmental uncertainty.
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George and Hawley. PR-015-09605-R01 Extended Low Flow Range Metering. Pipeline Research Council International, Inc. (PRCI), 2010. http://dx.doi.org/10.55274/r0010728.

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Natural gas meters are often used to measure flows below their minimum design flow rate. This can occur because of inaccurate flow projections, widely varying flow rates in the line, a lack of personnel available to change orifice plates, and other causes. The use of meters outside their design ranges can result in significant measurement errors. The objectives of this project were to examine parameters that contribute to measurement error at flow rates below 10% of a meters capacity, determine the expected range of error at these flow rates, and establish methods to reduce measurement error in this range. The project began with a literature search of prior studies of orifice, turbine, and ultrasonic meters for background information on their performance in low flows. Two conditions affecting multiple meter types were identified for study. First, temperature measurement errors in low flows can influence the accuracy of all three meter types, though the effect of a given temperature error can differ among the meter types. Second, thermally stratified flows at low flow rates are known to cause measurement errors in ultrasonic meters that cannot compensate for the resulting flow profiles, and the literature suggested that these flows could also affect orifice plates and turbine meters. Several possible ways to improve temperature measurements in low flows were also identified for further study. Next, an analytical study focused on potential errors due to inaccurate temperature measurements. Numerical tools were used to model a pipeline with different thermowell and RTD geometries. The goals were to estimate temperature measurement errors under different low-flow conditions, and to identify approaches to minimize temperature and flow rate errors. Thermal conduction from the pipe wall to the thermowell caused the largest predicted bias in measured temperature, while stratified temperatures in the flow caused relatively little temperature bias. Thermally isolating the thermowell from the pipe wall, or using a bare RTD, can minimize temperature bias, but are not usually practical approaches. Insulation of the meter run and the use of a finned thermowell design were practical methods predicted to potentially improve measurement accuracy, and were chosen for testing.
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Ihlenburg, Frank, and Ivo Babuska. Dispersion Analysis and Error Estimation of Galerkin Finite Element Methods for the Numerical Computation of Waves. Defense Technical Information Center, 1994. http://dx.doi.org/10.21236/ada290296.

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