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Journal articles on the topic 'Numerical differentiation'

Author: Grafiati

Published: 4 June 2021

Last updated: 30 July 2024

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1

Riachy, Samer, Mamadou Mboup, and Jean-Pierre Richard. "Multivariate numerical differentiation." Journal of Computational and Applied Mathematics 236, no. 6 (October 2011): 1069–89. http://dx.doi.org/10.1016/j.cam.2011.07.031.

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2

Chartrand, Rick. "Numerical Differentiation of Noisy, Nonsmooth Data." ISRN Applied Mathematics 2011 (May 11, 2011): 1–11. http://dx.doi.org/10.5402/2011/164564.

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We consider the problem of differentiating a function specified by noisy data. Regularizing the differentiation process avoids the noise amplification of finite-difference methods. We use total-variation regularization, which allows for discontinuous solutions. The resulting simple algorithm accurately differentiates noisy functions, including those which have a discontinuous derivative.

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3

Obradovic, Dragan, Lakshmi Narayan Mishra, and Vishnu Narayan Mishra. "Numerical Differentiation and Integration." JOURNAL OF ADVANCES IN PHYSICS 19 (January 25, 2021): 1–5. http://dx.doi.org/10.24297/jap.v19i.8938.

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There are several reasons why numerical differentiation and integration are used. The function that integrates f (x) can be known only in certain places, which is done by taking a sample. Some supercomputers and other computer applications sometimes need numerical integration for this very reason. The formula for the function to be integrated may be known, but it may be difficult or impossible to find the antiderivation that is an elementary function. One example is the function f (x) = exp (−x2), an antiderivation that cannot be written in elementary form. It is possible to find antiderivation symbolically, but it is much easier to find a numerical approximation than to calculate antiderivation (anti-derivative). This can be used if antiderivation is given as an unlimited array of products, or if the budget would require special features that are not available to computers.

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4

Ramm, Alexander G., and Alexandra B. Smirnova. "On stable numerical differentiation." Mathematics of Computation 70, no. 235 (March 9, 2001): 1131–54. http://dx.doi.org/10.1090/s0025-5718-01-01307-2.

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5

Huang, Xiaowei, Chuansheng Wu, and Jun Zhou. "Numerical differentiation by integration." Mathematics of Computation 83, no. 286 (June 4, 2013): 789–807. http://dx.doi.org/10.1090/s0025-5718-2013-02722-6.

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6

Herceg, Dragoslav, and Ljiljana Cvetković. "On a Numerical Differentiation." SIAM Journal on Numerical Analysis 23, no. 3 (June 1986): 686–91. http://dx.doi.org/10.1137/0723044.

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7

Ling, Leevan, and Qi Ye. "On meshfree numerical differentiation." Analysis and Applications 16, no. 05 (August 30, 2018): 717–39. http://dx.doi.org/10.1142/s021953051850001x.

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We combine techniques in meshfree methods and Gaussian process regressions to construct kernel-based estimators for numerical derivatives from noisy data. Specially, we construct meshfree estimators from normal random variables, which are defined by kernel-based probability measures induced from symmetric positive definite kernels, to reconstruct the unknown partial derivatives from scattered noisy data. Our developed theories give rise to Tikhonov regularization methods with a priori parameter, but the shape parameters of the kernels remain tunable. For that, we propose an error measure that is computable without the exact values of the derivative. This allows users to obtain a quasi-optimal kernel-based estimator by comparing the approximation quality of kernel-based estimators. Numerical examples in two dimensions and three dimensions are included to demonstrate the convergence behavior and effectiveness of the proposed numerical differentiation scheme.

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8

Davydov, Oleg, and Robert Schaback. "Minimal numerical differentiation formulas." Numerische Mathematik 140, no. 3 (May 31, 2018): 555–92. http://dx.doi.org/10.1007/s00211-018-0973-3.

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9

Murphy, Robin. "103.45 Improving elementary numerical integration using numerical differentiation." Mathematical Gazette 103, no. 558 (October 21, 2019): 548–56. http://dx.doi.org/10.1017/mag.2019.127.

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10

Hanke, Martin, and Otmar Scherzer. "Inverse Problems Light: Numerical Differentiation." American Mathematical Monthly 108, no. 6 (June 2001): 512. http://dx.doi.org/10.2307/2695705.

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11

Rédl, Jozef, and Dušan Páleš. "Numerical differentiation of stochastic function." Mathematics in Education, Research and Applications 2, no. 1 (October 30, 2016): 8–14. http://dx.doi.org/10.15414/meraa.2016.02.01.08-14.

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12

Riachy, Samer, Mamadou Mboup, and Jean-Pierre Richard. "Numerical differentiation on irregular grids." IFAC Proceedings Volumes 44, no. 1 (January 2011): 14–19. http://dx.doi.org/10.3182/20110828-6-it-1002.01941.

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13

Cheng, J., X. Z. Jia, and Y. B. Wang. "Numerical differentiation and its applications." Inverse Problems in Science and Engineering 15, no. 4 (June 2007): 339–57. http://dx.doi.org/10.1080/17415970600839093.

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14

Zhao, Zhenyu, and Zehong Meng. "Numerical differentiation for periodic functions." Inverse Problems in Science and Engineering 18, no. 7 (October 2010): 957–69. http://dx.doi.org/10.1080/17415977.2010.492517.

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15

Ly, B. L. "Numerical Differentiation Using Gaussian Quadrature." Journal of Engineering Mechanics 116, no. 11 (November 1990): 2568–72. http://dx.doi.org/10.1061/(asce)0733-9399(1990)116:11(2568).

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16

Dmitriev, V. I., and Zh G. Ingtem. "Numerical differentiation using spline functions." Computational Mathematics and Modeling 23, no. 3 (July 2012): 312–18. http://dx.doi.org/10.1007/s10598-012-9139-9.

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17

Hanke, Martin, and Otmar Scherzer. "Inverse Problems Light: Numerical Differentiation." American Mathematical Monthly 108, no. 6 (June 2001): 512–21. http://dx.doi.org/10.1080/00029890.2001.11919778.

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18

Yeadon, M. R. "Numerical differentiation of noisy data." Journal of Biomechanics 22, no. 10 (January 1989): 1104. http://dx.doi.org/10.1016/0021-9290(89)90526-5.

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19

Naumann, Uwe, Johannes Lotz, Klaus Leppkes, and Markus Towara. "Algorithmic Differentiation of Numerical Methods." ACM Transactions on Mathematical Software 41, no. 4 (October 26, 2015): 1–21. http://dx.doi.org/10.1145/2700820.

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20

Jauberteau, F., and J. L. Jauberteau. "Numerical differentiation with noisy signal." Applied Mathematics and Computation 215, no. 6 (November 2009): 2283–97. http://dx.doi.org/10.1016/j.amc.2009.08.042.

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21

Sharifi, M. A., M. R. Seif, and M. A. Hadi. "A Comparison Between Numerical Differentiation and Kalman Filtering for a Leo Satellite Velocity Determination." Artificial Satellites 48, no. 3 (September 1, 2013): 103–10. http://dx.doi.org/10.2478/arsa-2013-0009.

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Abstract The kinematic orbit is a time series of position vectors generally obtained from GPS observations. Velocity vector is required for satellite gravimetry application. It cannot directly be observed and should be numerically determined from position vectors. Numerical differentiation is usually employed for a satellite’s velocity, and acceleration determination. However, noise amplification is the single obstacle to the numerical differentiation. As an alternative, velocity vector is considered as a part of the state vector and is determined using the Kalman filter method. In this study, velocity vector is computed using the numerical differentiation (e.g., 9-point Newton interpolation scheme) and Kalman filtering for the GRACE twin satellites. The numerical results show that Kalman filtering yields more accurate results than numerical differentiation when they are compared with the intersatellite range-rate measurements.

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22

Busby, H. R., and D. M. Trujillo. "Numerical Experiments With a New Differentiation Filter." Journal of Biomechanical Engineering 107, no. 4 (November 1, 1985): 293–99. http://dx.doi.org/10.1115/1.3138558.

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A dynamic programming filter which provides estimates of the first and second derivative of empirical displacement data is investigated numerically. This filter uses a weighted least squares criteria in estimating the derivatives. The filter equations are presented together with several numerial examples. These examples are taken from references that proposed other techniques.

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23

Loktionov, A. P. "Numerical differentiation in the measurement model." Izmeritel`naya Tekhnika, no. 8 (2019): 14–19. http://dx.doi.org/10.32446/0368-1025it.2019-8-14-19.

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24

Voronin, E. G. "Numerical differentiation in photogrammetry equalization tasks." Geodesy and Cartography 981, no. 3 (April 20, 2022): 44–55. http://dx.doi.org/10.22389/0016-7126-2022-981-3-44-55.

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The author presents the results of studying numerical differentiation step influence in photogrammetric equalization tasks on the main characteristics of the resulting solution. A list of the main evaluated characteristics is presented and explanations of their role in the analysis of the photogrammetric equalization results are given. Using the example of several real routes of optical-electronic space survey, experimental calculations were performed, the purpose of which is to establish the dependence of the inverse photogrammetric serif’s main solution characteristics at the stage of numerical differentiation. The results of the equation calculations are analyzed and a conclusion is made on the instability of the estimated characteristics and not quite satisfactory outcome of equalization when assigning a step of numerical differentiation through known methods. A criterion for the optimality of the numerical differentiation step in photogrammetric equation tasks is proposed and an algorithm for calculating the step based on a new standard is developed. Its essence is explained and the graphical interpretation is given. Based on experimental calculations, the effectiveness of the developed criterion is confirmed.

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25

Mathews, John H. "Computer derivations of numerical differentiation formulae." International Journal of Mathematical Education in Science and Technology 34, no. 2 (January 2003): 280–87. http://dx.doi.org/10.1080/0020739031000158317.

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26

Prentice, J. S. C. "Numerical differentiation – a general purpose algorithm." International Journal of Mathematical Education in Science and Technology 44, no. 1 (January 15, 2013): 116–22. http://dx.doi.org/10.1080/0020739x.2012.662296.

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27

KING, J. THOMAS, and DIEGO A. MURIO. "Numerical Differentiation by Finite-Dimensional Regularition." IMA Journal of Numerical Analysis 6, no. 1 (1986): 65–85. http://dx.doi.org/10.1093/imanum/6.1.65.

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28

Hoffman, Peter, and K. C. Reddy. "Numerical Differentiation by High Order Interpolation." SIAM Journal on Scientific and Statistical Computing 8, no. 6 (November 1987): 979–87. http://dx.doi.org/10.1137/0908079.

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29

Syam, Muhammed I., and Hani I. Siyyam. "Numerical differentiation of implicitly defined curves." Journal of Computational and Applied Mathematics 108, no. 1-2 (August 1999): 131–44. http://dx.doi.org/10.1016/s0377-0427(99)00106-5.

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30

Isakov, V. N., and A. N. Kovalenko. "Local Methods of Numerical Signal Differentiation." Journal of Communications Technology and Electronics 64, no. 2 (February 2019): 111–18. http://dx.doi.org/10.1134/s1064226919020062.

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31

Murio, D. A., C. E. Mejía, and S. Zhan. "Discrete mollification and automatic numerical differentiation." Computers & Mathematics with Applications 35, no. 5 (March 1998): 1–16. http://dx.doi.org/10.1016/s0898-1221(98)00001-7.

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32

Hào, Dinh Nho, La Huu Chuong, and D. Lesnic. "Heuristic regularization methods for numerical differentiation." Computers & Mathematics with Applications 63, no. 4 (February 2012): 816–26. http://dx.doi.org/10.1016/j.camwa.2011.11.047.

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33

Loktionov, A. P. "Numerical Differentiation in the Measurement Model." Measurement Techniques 62, no. 8 (November 2019): 673–80. http://dx.doi.org/10.1007/s11018-019-01677-z.

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34

Shukla, Shyam S., and James F. Rusling. "Comparison of methods for numerical differentiation." TrAC Trends in Analytical Chemistry 4, no. 9 (October 1985): 229–33. http://dx.doi.org/10.1016/0165-9936(85)85009-3.

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35

Ahn, Soyoung, U. Jin Choi, and Alexander G. Ramm. "A scheme for stable numerical differentiation." Journal of Computational and Applied Mathematics 186, no. 2 (February 2006): 325–34. http://dx.doi.org/10.1016/j.cam.2005.02.002.

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36

Zhao, Zhenyu, Zehong Meng, and Guoqiang He. "A new approach to numerical differentiation." Journal of Computational and Applied Mathematics 232, no. 2 (October 2009): 227–39. http://dx.doi.org/10.1016/j.cam.2009.06.001.

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37

Bazhenov, V. G., and D. T. Chekmarev. "On index commutativity in numerical differentiation." USSR Computational Mathematics and Mathematical Physics 29, no. 3 (January 1989): 13–22. http://dx.doi.org/10.1016/0041-5553(89)90143-2.

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38

Murio, D. A. "Automatic numerical differentiation by discrete mollification." Computers & Mathematics with Applications 13, no. 4 (1987): 381–86. http://dx.doi.org/10.1016/0898-1221(87)90006-x.

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39

Eberhard, Peter, and Christian Bischof. "Automatic differentiation of numerical integration algorithms." Mathematics of Computation 68, no. 226 (April 1, 1999): 717–32. http://dx.doi.org/10.1090/s0025-5718-99-01027-3.

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40

Gordon, Sheldon P. "Some Surprising Errors in Numerical Differentiation." PRIMUS 22, no. 6 (August 2012): 437–50. http://dx.doi.org/10.1080/10511970.2010.536199.

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41

Fu, Chu-Li, Xiao-Li Feng, and Zhi Qian. "Wavelets and high order numerical differentiation." Applied Mathematical Modelling 34, no. 10 (October 2010): 3008–21. http://dx.doi.org/10.1016/j.apm.2010.01.009.

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42

Knowles, Ian, and Robert Wallace. "A variational method for numerical differentiation." Numerische Mathematik 70, no. 1 (March 1, 1995): 91–110. http://dx.doi.org/10.1007/s002110050111.

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43

Yang, Lu. "A perturbation method for numerical differentiation." Applied Mathematics and Computation 199, no. 1 (May 2008): 368–74. http://dx.doi.org/10.1016/j.amc.2007.09.066.

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44

Macleod, Allan J. "Numerical differentiation by the regularization method." Communications in Applied Numerical Methods 2, no. 6 (November 1986): 625–32. http://dx.doi.org/10.1002/cnm.1630020611.

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45

Omeragić, Dževat, and Peter P. Silvester. "Numerical differentiation in magnetic field postprocessing." International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 9, no. 1-2 (January 1996): 99–113. http://dx.doi.org/10.1002/(sici)1099-1204(199601)9:1/2<99::aid-jnm230>3.0.co;2-k.

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46

Trunec, D. "The Numerical Differentiation of Probe Characteristic." Contributions to Plasma Physics 32, no. 5 (1992): 523–34. http://dx.doi.org/10.1002/ctpp.2150320505.

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47

Fukushima, Toshio, and Toshimichi Shirai. "Numerical Convolution Method in Time Domain and Its Application to Nonrigid Earth Nutation Theory." International Astronomical Union Colloquium 178 (2000): 595–605. http://dx.doi.org/10.1017/s0252921100061765.

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AbstractWe developed a numerical method to incorporate nonrigid effects into a nutation theory of the rigid Earth. Here we assume that the nonrigid effects are based on a linear response theory and its transfer function is expressed as a rational function of frequency. The method replaces the convolution of the transfer function in the frequency domain by the corresponding integro-differential operations in the time domain numerically; namely multiplying the polynomial in the frequency domain by the numerical differentiations in the time domain and multiplying the fractions in the frequency domain by the numerical integrations with a suitable kernel in the time domain. In replacing by the integrations, the method requires the determination of the coefficients of free oscillation. This is done by a least-squares method to fit the theory incorporated with the nonrigid effects to the observational data, whose availability is also assumed. The numerical differentiation and integration are effectively computed by means of the symmetric formulas of differentiation and integration. Numerical tests showed that the method is sufficiently precise to reproduce the analytically convolved nutation at the level of 10 nano arcseconds by using the 9-point central difference formulas and the 8-point symmetric integration formula to cover the period of 15 years with 1.5-hour stepsize. Since we only require the rigid Earth nutation theory to be expressed as a numerical table of time, this method enables one to create a purely numerical theory of nutation of the nonrigid Earth.

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48

Russell, Robert D., and Weiwei Sun. "Spline Collocation Differentiation Matrices." SIAM Journal on Numerical Analysis 34, no. 6 (December 1997): 2274–87. http://dx.doi.org/10.1137/s0036142994277985.

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49

Sneddon, G. E. "Second-Order Spectral Differentiation Matrices." SIAM Journal on Numerical Analysis 33, no. 6 (December 1996): 2468–87. http://dx.doi.org/10.1137/s0036142994264237.

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50

Olver, Sheehan. "GMRES for the Differentiation Operator." SIAM Journal on Numerical Analysis 47, no. 5 (January 2009): 3359–73. http://dx.doi.org/10.1137/080724964.

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