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Journal articles on the topic 'Numerical error analysis'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 February 2022

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1

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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2

Faber, Vance, and Thomas A. Manteuffel. "Orthogonal Error Methods." SIAM Journal on Numerical Analysis 24, no. 1 (1987): 170–87. http://dx.doi.org/10.1137/0724014.

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3

Ditkowski, Adi, Sigal Gottlieb, and Zachary J. Grant. "Two-Derivative Error Inhibiting Schemes and Enhanced Error Inhibiting Schemes." SIAM Journal on Numerical Analysis 58, no. 6 (2020): 3197–225. http://dx.doi.org/10.1137/19m1306129.

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4

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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5

Kuperberg, Greg. "Numerical Cubature Using Error-Correcting Codes." SIAM Journal on Numerical Analysis 44, no. 3 (2006): 897–907. http://dx.doi.org/10.1137/040615572.

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6

Reich, Sebastian. "Backward Error Analysis for Numerical Integrators." SIAM Journal on Numerical Analysis 36, no. 5 (1999): 1549–70. http://dx.doi.org/10.1137/s0036142997329797.

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7

Connors, Jeffrey M., Jeffrey W. Banks, Jeffrey A. Hittinger, and Carol S. Woodward. "A Method to Calculate Numerical Errors Using Adjoint Error Estimation for Linear Advection." SIAM Journal on Numerical Analysis 51, no. 2 (2013): 894–926. http://dx.doi.org/10.1137/110845100.

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8

Wetton, Brian R. "Error Analysis of Pressure Increment Schemes." SIAM Journal on Numerical Analysis 38, no. 1 (2000): 160–69. http://dx.doi.org/10.1137/s0036142998338538.

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9

Axelsson, O., and L. Kolotilina. "Monotonicity and Discretization Error Estimates." SIAM Journal on Numerical Analysis 27, no. 6 (1990): 1591–611. http://dx.doi.org/10.1137/0727093.

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10

Aves, Mark A., David F. Griffiths, and Desmond J. Higham. "Does Error Control Suppress Spuriosity?" SIAM Journal on Numerical Analysis 34, no. 2 (1997): 756–78. http://dx.doi.org/10.1137/s0036142994276980.

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11

Estep, Donald. "A Posteriori Error Bounds and Global Error Control for Approximation of Ordinary Differential Equations." SIAM Journal on Numerical Analysis 32, no. 1 (1995): 1–48. http://dx.doi.org/10.1137/0732001.

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12

Liu, Wenbin, and Ningning Yan. "On Quasi-Norm Interpolation Error Estimation And A Posteriori Error Estimates for p-Laplacian." SIAM Journal on Numerical Analysis 40, no. 5 (2002): 1870–95. http://dx.doi.org/10.1137/s0036142901393589.

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13

Harťanský, R., V. Smieško, and L. Maršálka. "Numerical Analysis of Isotropy Electromagnetic Sensor Measurement Error." Measurement Science Review 13, no. 6 (2013): 311–14. http://dx.doi.org/10.2478/msr-2013-0046.

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Abstract The article deals with classification and quantification of electromagnetic field measurement errors in case an isotropic sensor as a field probe is used. The focus is mainly on the error of measurement method, resulting from mutual interaction of the field probe sensors associated with the origin of the so-called mutual impedance.

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14

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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15

Weideman, J. A. C. "Computation of the Complex Error Function." SIAM Journal on Numerical Analysis 31, no. 5 (1994): 1497–518. http://dx.doi.org/10.1137/0731077.

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16

Dieci, Luca, and Erik S. Van Vleck. "On the Error in QR Integration." SIAM Journal on Numerical Analysis 46, no. 3 (2008): 1166–89. http://dx.doi.org/10.1137/06067818x.

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17

Hild, Patrick, and Vanessa Lleras. "Residual Error Estimators for Coulomb Friction." SIAM Journal on Numerical Analysis 47, no. 5 (2009): 3550–83. http://dx.doi.org/10.1137/070711554.

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18

Singler, John R. "New POD Error Expressions, Error Bounds, and Asymptotic Results for Reduced Order Models of Parabolic PDEs." SIAM Journal on Numerical Analysis 52, no. 2 (2014): 852–76. http://dx.doi.org/10.1137/120886947.

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19

Scaillet, Stéphane. "Numerical error analysis in 40Ar/39Ar dating." Chemical Geology 162, no. 3-4 (2000): 269–98. http://dx.doi.org/10.1016/s0009-2541(99)00149-7.

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20

Stummel, F. "Book Review: Error analysis in numerical processes." Bulletin of the American Mathematical Society 28, no. 1 (1993): 204–7. http://dx.doi.org/10.1090/s0273-0979-1993-00357-4.

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21

Fu, Zhoulai, Zhaojun Bai, and Zhendong Su. "Automated backward error analysis for numerical code." ACM SIGPLAN Notices 50, no. 10 (2015): 639–54. http://dx.doi.org/10.1145/2858965.2814317.

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22

Takeuchi, K., and N. Sasamoto. "Numerical error analysis of direct integration method." Transport Theory and Statistical Physics 15, no. 1-2 (1986): 117–34. http://dx.doi.org/10.1080/00411458608210447.

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23

Symes, William W., and Tetyana Vdovina. "Interface error analysis for numerical wave propagation." Computational Geosciences 13, no. 3 (2009): 363–71. http://dx.doi.org/10.1007/s10596-008-9124-8.

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24

Papakostas, G. A., Y. S. Boutalis, C. N. Papaodysseus, and D. K. Fragoulis. "Numerical error analysis in Zernike moments computation." Image and Vision Computing 24, no. 9 (2006): 960–69. http://dx.doi.org/10.1016/j.imavis.2006.02.015.

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25

Stengle, Gilbert. "Error analysis of a randomized numerical method." Numerische Mathematik 70, no. 1 (1995): 119–28. http://dx.doi.org/10.1007/s002110050113.

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26

Obi, Wilson C. "Error Analysis of a Laplace Transform Inversion Procedure." SIAM Journal on Numerical Analysis 27, no. 2 (1990): 457–69. http://dx.doi.org/10.1137/0727028.

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27

Stenberg, Rolf, and Manil Suri. "An hp Error Analysis of MITC Plate Elements." SIAM Journal on Numerical Analysis 34, no. 2 (1997): 544–68. http://dx.doi.org/10.1137/s0036142994278486.

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28

Fink, P. James, and Werner C. Rheinboldt. "Local Error Estimates for Parametrized Nonlinear Equations." SIAM Journal on Numerical Analysis 22, no. 4 (1985): 729–35. http://dx.doi.org/10.1137/0722044.

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29

Bank, Randolph E., and Donald J. Rose. "Some Error Estimates for the Box Method." SIAM Journal on Numerical Analysis 24, no. 4 (1987): 777–87. http://dx.doi.org/10.1137/0724050.

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30

Weideman, J. A. C. "Erratum: Computation of the Complex Error Function." SIAM Journal on Numerical Analysis 32, no. 1 (1995): 330–31. http://dx.doi.org/10.1137/0732014.

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31

Carstensen, Carsten, Leszek Demkowicz, and Jay Gopalakrishnan. "A Posteriori Error Control for DPG Methods." SIAM Journal on Numerical Analysis 52, no. 3 (2014): 1335–53. http://dx.doi.org/10.1137/130924913.

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32

Cezikturk, Ozlem. "Spreadsheets for Numerical Analysis: A conceptual tool." Academic Perspective Procedia 2, no. 1 (2019): 57–65. http://dx.doi.org/10.33793/acperpro.02.01.12.

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Using spreadsheets for mathematics education is not a new idea. However, analysing student logical mistakes for preserving error types and conceptual decision making would be first to study. A class of students were given two home works in order for grading. They were told to carry on calculations via spreadsheets and give the homework exam with spreadsheet file. In H1, questions were on root finding and solution of simultaneous equations. In H2, questions were on line and curve approximations, interpolation, numerical integration and numerical differentiation. These files are analysed by content analysis of qualitative method. By this way, it is hypothesized that they would do similar errors regarding error types and their decision making would inform us about their conceptual learning.

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33

Samrowski, Tatiana. "Combined Error Estimates in the Case of Dimension Reduction." Computational Methods in Applied Mathematics 14, no. 1 (2014): 113–34. http://dx.doi.org/10.1515/cmam-2013-0024.

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Abstract. We consider the stationary reaction-diffusion problem in a domain $\Omega \subset \mathbb {R}^3$ having the size along one coordinate direction essentially smaller than along the others. By an energy type argumentation, different simplified models of lower dimension can be deduced and solved numerically. For these models, we derive a guaranteed upper bound of the difference between the exact solution of the original problem and a three-dimensional reconstruction generated by the solution of a dimensionally reduced problem. This estimate of the total error is determined as the sum of discretization and modeling errors, which are both explicit and computable. The corresponding discretization errors are estimated by a posteriori estimates of the functional type. Modeling error majorants are also explicitly evaluated. Hence, a numerical strategy based on the balancing modeling and discretization errors can be derived in order to provide an economical way of getting an approximate solution with an a priori given accuracy. Numerical tests are presented and discussed.

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34

Monk, P. B., and O. Vacus. "Error Estimates for a Numerical Scheme for Ferromagnetic Problems." SIAM Journal on Numerical Analysis 36, no. 3 (1999): 696–718. http://dx.doi.org/10.1137/s0036142997324228.

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35

Shen, Jie, and Li-Lian Wang. "Error Analysis for Mapped Legendre Spectral and Pseudospectral Methods." SIAM Journal on Numerical Analysis 42, no. 1 (2004): 326–49. http://dx.doi.org/10.1137/s0036142903422065.

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36

Katsoulakis, Markos A., Petr Plecháč, and Alexandros Sopasakis. "Error Analysis of Coarse‐Graining for Stochastic Lattice Dynamics." SIAM Journal on Numerical Analysis 44, no. 6 (2006): 2270–96. http://dx.doi.org/10.1137/050637339.

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37

Bank, Randolph E., and Bruno D. Welfert. "A Posteriori Error Estimates for the Stokes Problem." SIAM Journal on Numerical Analysis 28, no. 3 (1991): 591–623. http://dx.doi.org/10.1137/0728033.

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38

Duran, Ricardo, Maria Amelia Muschietti, and Rodolfo Rodriguez. "Asymptotically Exact Error Estimators for Rectangular Finite Elements." SIAM Journal on Numerical Analysis 29, no. 1 (1992): 78–88. http://dx.doi.org/10.1137/0729005.

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39

Bank, Randolph E., and R. Kent Smith. "A Posteriori Error Estimates Based on Hierarchical Bases." SIAM Journal on Numerical Analysis 30, no. 4 (1993): 921–35. http://dx.doi.org/10.1137/0730048.

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40

Dubuc, B., and S. Dubuc. "Error Bounds on the Estimation of Fractal Dimension." SIAM Journal on Numerical Analysis 33, no. 2 (1996): 602–26. http://dx.doi.org/10.1137/0733032.

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41

Hickernell, Fred J. "Quadrature Error Bounds with Applications to Lattice Rules." SIAM Journal on Numerical Analysis 33, no. 5 (1996): 1995–2016. http://dx.doi.org/10.1137/s0036142994261439.

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42

Tautenhahn, Ulrich. "Error Estimates for Regularization Methods in Hilbert Scales." SIAM Journal on Numerical Analysis 33, no. 6 (1996): 2120–30. http://dx.doi.org/10.1137/s0036142994269411.

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43

Knyazev, Andrew V., and John E. Osborn. "New A Priori FEM Error Estimates for Eigenvalues." SIAM Journal on Numerical Analysis 43, no. 6 (2006): 2647–67. http://dx.doi.org/10.1137/040613044.

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44

Schatz, Alfred H. "Pointwise Error Estimates and Asymptotic Error Expansion Inequalities for the Finite Element Method on Irregular Grids: Part II. Interior Estimates." SIAM Journal on Numerical Analysis 38, no. 4 (2000): 1269–93. http://dx.doi.org/10.1137/s0036142997324800.

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45

Toutounian, F., Emran Tohidi, and A. Kilicman. "Fourier Operational Matrices of Differentiation and Transmission: Introduction and Applications." Abstract and Applied Analysis 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/198926.

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This paper introduces Fourier operational matrices of differentiation and transmission for solving high-order linear differential and difference equations with constant coefficients. Moreover, we extend our methods for generalized Pantograph equations with variable coefficients by using Legendre Gauss collocation nodes. In the case of numerical solution of Pantograph equation, an error problem is constructed by means of the residual function and this error problem is solved by using the mentioned collocation scheme. When the exact solution of the problem is not known, the absolute errors can be computed approximately by the numerical solution of the error problem. The reliability and efficiency of the presented approaches are demonstrated by several numerical examples, and also the results are compared with different methods.

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46

Ku, JaEun. "Pointwise Error Estimates for First-Order div Least-Squares Finite Element Methods and Applications to Superconvergence and A Posteriori Error Estimators." SIAM Journal on Numerical Analysis 49, no. 2 (2011): 521–40. http://dx.doi.org/10.1137/090762191.

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47

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

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Analytical formulas for the gravity anomaly of a uniform polyhedral body are subject to numerical error that increases with distance from the target, while the anomaly decreases. This leads to a limited range of target distances in which the formulas are operational, beyond which the calculations are dominated by rounding error. We analyze the sources of error and propose a combination of numerical and analytical procedures that exhibit advantages over existing methods, namely (1) errors that diminish with distance, (2) enhanced operating range, and (3) algorithmic simplicity. The latter is achieved by avoiding the need to transform coordinates and the need to discriminate between projected observation points that lie inside, on, or outside a target facet boundary. Our error analysis is verified in computations based on a published code and on a code implementing our methods. The former requires a numerical precision of one part in [Formula: see text] (double precision) in problems of geophysical interest, whereas our code requires a precision of one part in [Formula: see text] (single precision) to give comparable results, typically in half the execution time.

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48

Li, Guangning, Dinesh Bhatia, Min Xu, and Jian Wang. "Grid Convergence Analysis for MUSCL-based Numerical Scheme in Shockwave-containing Flows." MATEC Web of Conferences 257 (2019): 02001. http://dx.doi.org/10.1051/matecconf/201925702001.

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This paper investigated the influence of limiter functions widely utilized in MUSCL-type (Monotone Upstream-centred Schemes for Conservation Laws) upwind numerical schemes on the solution accuracy of shockwave-containing flows. An incident shock interacting with laminar boundary layer developed on a flat plate was numerically simulated with the in-house developed code. A mixed-order grid convergence study was performed to assess the spatial errors of different limiters in simulating the selected shockwave-containing flow on flat plate. The conclusions are that, limiter functions implemented in the current in-house code play the critical roles in accurately predicting shockwave-containing flows. The mixed-order error estimator based on grid convergence study was proved to be applicable to evaluate the spatial errors of shockwave-containing flows, where the shock could reduce the nominal second- or third-order accuracy to first-order. The mixed-order estimator is conservative in the sense that the actual error is less than the error estimated, in the examined case.

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49

Sloan, Ian H. "Error analysis of boundary integral methods." Acta Numerica 1 (January 1992): 287–339. http://dx.doi.org/10.1017/s0962492900002294.

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Many of the boundary value problems traditionally cast as partial differential equations can be reformulated as integral equations over the boundary. After an introduction to boundary integral equations, this review describes some of the methods which have been proposed for their approximate solution. It discusses, as simply as possible, some of the techniques used in their error analysis, and points to areas in which the theory is still unsatisfactory.

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50

Han, Xiaoying, Jinglai Li, and Dongbin Xiu. "Error analysis for numerical formulation of particle filter." Discrete and Continuous Dynamical Systems - Series B 20, no. 5 (2015): 1337–54. http://dx.doi.org/10.3934/dcdsb.2015.20.1337.

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