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Journal articles on the topic 'Padé approximation'

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Published: 4 June 2021
Last updated: 30 May 2022

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1

Khodier, Ahmed M. M. "Perturbed padé approximation." International Journal of Computer Mathematics 74, no. 2 (January 2000): 247–53. http://dx.doi.org/10.1080/00207160008804938.

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2

Guillaume, Philippe, and Alain Huard. "Multivariate Padé approximation." Journal of Computational and Applied Mathematics 121, no. 1-2 (September 2000): 197–219. http://dx.doi.org/10.1016/s0377-0427(00)00337-x.

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3

Brezinski, Claude. "Partial Padé approximation." Journal of Approximation Theory 54, no. 2 (August 1988): 210–33. http://dx.doi.org/10.1016/0021-9045(88)90020-2.

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4

Fasondini, Marco, Nicholas Hale, Rene Spoerer, and J. A. C. Weideman. "Quadratic Padé Approximation: Numerical Aspects and Applications." Computer Research and Modeling 11, no. 6 (December 2019): 1017–31. http://dx.doi.org/10.20537/2076-7633-2019-11-6-1017-1031.

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5

Daras, Nicholas J. "Composed Padé-type approximation." Journal of Computational and Applied Mathematics 134, no. 1-2 (September 2001): 95–112. http://dx.doi.org/10.1016/s0377-0427(00)00531-8.

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6

Allouche, Hassane, Ebby Mint El Agheb, and Noura Ghanou. "Adapted multivariate Padé approximation." Applied Numerical Mathematics 62, no. 9 (September 2012): 1061–76. http://dx.doi.org/10.1016/j.apnum.2011.07.007.

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7

Bultheel, Adhemar, and Marc Van Barel. "Minimal vector Padé approximation." Journal of Computational and Applied Mathematics 32, no. 1-2 (November 1990): 27–37. http://dx.doi.org/10.1016/0377-0427(90)90413-t.

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8

Song, Hanjie, Yingjie Gao, Jinhai Zhang, and Zhenxing Yao. "Long-offset moveout for VTI using Padé approximation." GEOPHYSICS 81, no. 5 (September 2016): C219—C227. http://dx.doi.org/10.1190/geo2015-0094.1.

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The approximation of normal moveout is essential for estimating the anisotropy parameters of the transversally isotropic media with vertical symmetry axis (VTI). We have approximated the long-offset moveout using the Padé approximation based on the higher order Taylor series coefficients for VTI media. For a given anellipticity parameter, we have the best accuracy when the numerator is one order higher than the denominator (i.e., [[Formula: see text]]); thus, we suggest using [4/3] and [7/6] orders for practical applications. A [7/6] Padé approximation can handle a much larger offset and stronger anellipticity parameter. We have further compared the relative traveltime errors between the Padé approximation and several approximations. Our method shows great superiority to most existing methods over a wide range of offset (normalized offset up to 2 or offset-to-depth ratio up to 4) and anellipticity parameter (0–0.5). The Padé approximation provides us with an attractive high-accuracy scheme with an error that is negligible within its convergence domain. This is important for reducing the error accumulation especially for deeper substructures.
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9

Sadaka, R. "Padé approximation of vector functions." Applied Numerical Mathematics 21, no. 1 (May 1996): 57–70. http://dx.doi.org/10.1016/0168-9274(96)00002-5.

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10

Brookes, Richard G. "The quadratic hermite-padé approximation." Bulletin of the Australian Mathematical Society 40, no. 3 (December 1989): 489. http://dx.doi.org/10.1017/s0004972700017561.

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11

Gonnet, Pedro, Stefan Güttel, and Lloyd N. Trefethen. "Robust Padé Approximation via SVD." SIAM Review 55, no. 1 (January 2013): 101–17. http://dx.doi.org/10.1137/110853236.

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12

Cai, Jialin, Justin B. King, Brian M. Merrick, and Thomas J. Brazil. "Padé-Approximation-Based Behavioral Modeling." IEEE Transactions on Microwave Theory and Techniques 61, no. 12 (December 2013): 4418–27. http://dx.doi.org/10.1109/tmtt.2013.2287677.

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13

Stahl, Herbert. "Spurious poles in Padé approximation." Journal of Computational and Applied Mathematics 99, no. 1-2 (November 1998): 511–27. http://dx.doi.org/10.1016/s0377-0427(98)00180-0.

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14

Tourigny, Y., and P. G. Drazin. "The dynamics of Padé approximation." Nonlinearity 15, no. 3 (April 3, 2002): 787–805. http://dx.doi.org/10.1088/0951-7715/15/3/316.

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15

Brezinski, C., Ufr Ieea, and J. Van Iseghem. "A Taste of Padé Approximation." Acta Numerica 4 (January 1995): 53–103. http://dx.doi.org/10.1017/s096249290000252x.

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16

de Bruin, M. "Padé approximation and its applications." Acta Applicandae Mathematica 5, no. 2 (February 1986): 200–203. http://dx.doi.org/10.1007/bf00046591.

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17

Faiz, Ahmad. "Orthogonal polynomials and Padé approximation." Journal of Shanghai University (English Edition) 2, no. 2 (June 1998): 108–11. http://dx.doi.org/10.1007/s11741-998-0072-2.

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18

Chip, M. M. "Padé approximation and generalized moments." Journal of Mathematical Sciences 90, no. 5 (July 1998): 2416–20. http://dx.doi.org/10.1007/bf02433976.

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19

Lorentzen, Lisa. "Padé approximation and continued fractions." Applied Numerical Mathematics 60, no. 12 (December 2010): 1364–70. http://dx.doi.org/10.1016/j.apnum.2010.03.016.

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20

Brezinski, Claude. "Duality in Padé-type approximation." Journal of Computational and Applied Mathematics 30, no. 3 (July 1990): 351–57. http://dx.doi.org/10.1016/0377-0427(90)90285-8.

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21

Ambroladze, Amiran, and Hans Wallin. "Approximation by repeated Padé approximants." Journal of Computational and Applied Mathematics 62, no. 3 (September 1995): 353–58. http://dx.doi.org/10.1016/0377-0427(94)00112-3.

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22

Matala-Aho, Tapani, and Keijo Väänänen. "On approximation measures of q-logarithms." Bulletin of the Australian Mathematical Society 58, no. 1 (August 1998): 15–31. http://dx.doi.org/10.1017/s000497270003197x.

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23

Capozziello, S., R. D’Agostino, and O. Luongo. "High-redshift cosmography: auxiliary variables versus Padé polynomials." Monthly Notices of the Royal Astronomical Society 494, no. 2 (April 7, 2020): 2576–90. http://dx.doi.org/10.1093/mnras/staa871.

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ABSTRACT Cosmography becomes non-predictive when cosmic data span beyond the redshift limit z ≃ 1. This leads to a strong convergence issue that jeopardizes its viability. In this work, we critically compare the two main solutions of the convergence problem, i.e. the y-parametrizations of the redshift and the alternatives to Taylor expansions based on Padé series. In particular, among several possibilities, we consider two widely adopted parametrizations, namely y1 = 1−a and $y_2=\arctan (a^{-1}-1)$, being a the scale factor of the Universe. We find that the y2-parametrization performs relatively better than the y1-parametrization over the whole redshift domain. Even though y2 overcomes the issues of y1, we get that the most viable approximations of the luminosity distance dL(z) are given in terms of Padé approximations. In order to check this result by means of cosmic data, we analyse the Padé approximations up to the fifth order, and compare these series with the corresponding y-variables of the same orders. We investigate two distinct domains involving Monte Carlo analysis on the Pantheon Superovae Ia data, H(z) and shift parameter measurements. We conclude that the (2,1) Padé approximation is statistically the optimal approach to explain low- and high-redshift data, together with the fifth-order y2-parametrization. At high redshifts, the (3,2) Padé approximation cannot be fully excluded, while the (2,2) Padé one is essentially ruled out.
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24

Pratiwi, Indah Nur, Mohammad Syamsu Rosid, and Humbang Purba. "Reducing Residual Moveout for Long Offset Data in VTI Media Using Padé Approximation." E3S Web of Conferences 125 (2019): 15005. http://dx.doi.org/10.1051/e3sconf/201912515005.

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Modification of the hyperbolic travel time equation into non-hyperbolic travel time equation is important to increase the reduction residual moveout for long offset data. Some researchers have modified hyperbolic travel time equation into a non-hyperbolic travel time equation to obtain a more accurate value NMO velocity and parameter an-ellipticity or etha on the large offset to depth ratio (ODR) so that the residual moveout value is smaller mainly in large offset to depth ratio. The aims of research is to increase the reduction value of error residue at long offset data using Padé approximation then compare with several approximations. The method used in this study is to conduct forward modeling of the subsurface coating structure. The results of the three-dimensional analysis show that the Padé approximation has the best accuracy compared to the other travel time equations for ODR value up to 4 with an-ellipticity parameter is varying from 0 to 0.5. Testing of synthetic data for single layer on vertical transverse isotropy (VTI) medium obtained the maximum residual error value produced by the Padé approximation is 0.25% in ODR=4. Therefore, Padé approximation is better than other methods for reducing residual moveout.
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25

Belantari, A. "Error estimate in vector Padé approximation." Applied Numerical Mathematics 8, no. 6 (December 1991): 457–68. http://dx.doi.org/10.1016/0168-9274(91)90108-c.

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26

Khodier, Ahmed M. M. "Perturbed Padé approximation with high accuracy." Applied Mathematics and Computation 148, no. 3 (January 2004): 753–57. http://dx.doi.org/10.1016/s0096-3003(02)00935-9.

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27

Paszkowski, Stefan. "Recurrence relations in Padé-Hermite approximation." Journal of Computational and Applied Mathematics 19, no. 1 (July 1987): 99–107. http://dx.doi.org/10.1016/s0377-0427(87)80014-6.

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28

Allen, Edward J. "On the Error in Padé Approximation." SIAM Review 29, no. 2 (June 1987): 299. http://dx.doi.org/10.1137/1029049.

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29

Astafyeva, A. V., and A. P. Starovoitov. "Hermite-Padé approximation of exponential functions." Sbornik: Mathematics 207, no. 6 (June 30, 2016): 769–91. http://dx.doi.org/10.1070/sm8470.

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30

Farr, Jeffrey B., and Shuhong Gao. "Gröbner bases and generalized Padé approximation." Mathematics of Computation 75, no. 253 (October 12, 2005): 461–74. http://dx.doi.org/10.1090/s0025-5718-05-01790-4.

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31

TANG, J., and J. R. NORRIS. "Padé approximation and linear prediction methods." Nature 333, no. 6170 (May 1988): 216. http://dx.doi.org/10.1038/333216a0.

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32

Brezinski, C. "From numerical quadrature to Padé approximation." Applied Numerical Mathematics 60, no. 12 (December 2010): 1209–20. http://dx.doi.org/10.1016/j.apnum.2010.06.001.

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33

Xu, Guo-liang, and Adhemar Bultheel. "Matrix padé approximation: definitions and properties." Linear Algebra and its Applications 137-138 (August 1990): 67–136. http://dx.doi.org/10.1016/0024-3795(90)90127-x.

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34

Paszkowski, Stefan. "Recurrence relations in Padé—Hermite approximation." Journal of Computational and Applied Mathematics 19, no. 1 (July 1987): 99–107. http://dx.doi.org/10.1016/0377-0427(87)90177-4.

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35

González-Vera, Pablo, and Olav Njåstad. "Szegö functions and multipoint Padé approximation." Journal of Computational and Applied Mathematics 32, no. 1-2 (November 1990): 107–16. http://dx.doi.org/10.1016/0377-0427(90)90422-v.

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36

Fitzpatrick, P. "A theoretical basis for Padé approximation." Irish Mathematical Society Bulletin 0030 (1993): 6–17. http://dx.doi.org/10.33232/bims.0030.6.17.

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37

Avram, Florin, Andras Horváth, Serge Provost, and Ulyses Solon. "On the Padé and Laguerre–Tricomi–Weeks Moments Based Approximations of the Scale Function W and of the Optimal Dividends Barrier for Spectrally Negative Lévy Risk Processes." Risks 7, no. 4 (December 11, 2019): 121. http://dx.doi.org/10.3390/risks7040121.

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This paper considers the Brownian perturbed Cramér–Lundberg risk model with a dividends barrier. We study various types of Padé approximations and Laguerre expansions to compute or approximate the scale function that is necessary to optimize the dividends barrier. We experiment also with a heavy-tailed claim distribution for which we apply the so-called “shifted” Padé approximation.
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38

Bosuwan, Nattapong. "On Row Sequences of Hermite–Padé Approximation and Its Generalizations." Mathematics 8, no. 3 (March 6, 2020): 366. http://dx.doi.org/10.3390/math8030366.

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Hermite–Padé approximation has been a mainstay of approximation theory since the concept was introduced by Charles Hermite in his proof of the transcendence of e in 1873. This subject occupies a large place in the literature and it has applications in different subjects. Most of the studies of Hermite–Padé approximation have mainly concentrated on diagonal sequences. Recently, there were some significant contributions in the direction of row sequences of Type II Hermite–Padé approximation. Moreover, various generalizations of Type II Hermite–Padé approximation were introduced and studied on row sequences. The purpose of this paper is to reflect the current state of the study of Type II Hermite–Padé approximation and its generalizations on row sequences. In particular, we focus on the relationship between the convergence of zeros of the common denominators of such approximants and singularities of the vector of approximated functions. Some conjectures concerning these studies are posed.
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39

Bercu, Gabriel. "New Refinements for the Error Function with Applications in Diffusion Theory." Symmetry 12, no. 12 (December 6, 2020): 2017. http://dx.doi.org/10.3390/sym12122017.

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In this paper we provide approximations for the error function using the Padé approximation method and the Fourier series method. These approximations have simple forms and acceptable bounds for the absolute error. Then we use them in diffusion theory.
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40

Hirata-Kohno, Noriko. "Diophantine approximation." Sugaku Expositions 34, no. 2 (October 12, 2021): 205–29. http://dx.doi.org/10.1090/suga/463.

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This article gives an introductory survey of recent progress on Diophantine problems, especially consequences coming from Schmidt’s subspace theorem, Baker’s transcendence method and Padé approximation. We present fundamental properties around Diophantine approximation and how it yields results in number theory.
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41

Yamada, Hiroaki S., and Kensuke S. Ikeda. "A Numerical Test of Padé Approximation for Some Functions with Singularity." International Journal of Computational Mathematics 2014 (November 20, 2014): 1–17. http://dx.doi.org/10.1155/2014/587430.

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The aim of this study is to examine some numerical tests of Padé approximation for some typical functions with singularities such as simple pole, essential singularity, brunch cut, and natural boundary. As pointed out by Baker, it was shown that the simple pole and the essential singularity can be characterized by the poles of the Padé approximation. However, it was not fully clear how the Padé approximation works for the functions with the branch cut or the natural boundary. In the present paper, it is shown that the poles and zeros of the Padé approximated functions are alternately lined along the branch cut if the test function has branch cut, and poles are also distributed around the natural boundary for some lacunary power series and random power series which rigorously have a natural boundary on the unit circle. On the other hand, Froissart doublets due to numerical errors and/or external noise also appear around the unit circle in the Padé approximation. It is also shown that the residue calculus for the Padé approximated functions can be used to confirm the numerical accuracy of the Padé approximation and quasianalyticity of the random power series.
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42

Kirit Mehta, Avani, and R. Swarnalatha. "Adopting pade approximation for first order plus dead time models for blending process." International Journal of Engineering & Technology 7, no. 4 (October 6, 2018): 2800. http://dx.doi.org/10.14419/ijet.v7i4.18089.

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Dead-time is common to real time processes and occurs when the process variable doesn’t acknowledge to any changes in the set point. Existence of dead time in the systems poses a challenge to control and stabilize, especially in a control feedback loop. Padé approximation provides a determinate approximation of the dead time in the continuous process systems, which can be utilized in the further simulations of equivalent First Order plus Dead Time Models. However, the standard Padé approximation with the same numerator- denominator derivative power, exhibits a jolt at time t=0. This gives an inaccurate approximation of the dead time. To avoid this phenomenon, increasing orders of Padé approximation is applied. In the following manuscript, equivalent First Order plus Dead-Time models of two blending systems of orders four and seven are analysed for the same. As the orders of the Padé approximation increases, the accuracy of the response also increases. The oscillations are increased on a much smaller scale rather than having one big dip in the negative region (as observed in the first few orders of Padé approximation), and the approximation tries to synchronize with the desired response curve in the positive region. All the simulations are done in MATLAB.
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43

Andrianov, I. V., J. Awrejcewicz, and A. O. Ivankov. "On an elastic dissipation model as continuous approximation for discrete media." Mathematical Problems in Engineering 2006 (2006): 1–8. http://dx.doi.org/10.1155/mpe/2006/27373.

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Construction of an accurate continuous model for discrete media is an important topic in various fields of science. We deal with a 1D differential-difference equation governing the behavior of ann-mass oscillator with linear relaxation. It is known that a string-type approximation is justified for low part of frequency spectra of a continuous model, but for free and forced vibrations a solution of discrete and continuous models can be quite different. A difference operator makes analysis difficult due to its nonlocal form. Approximate equations can be obtained by replacing the difference operators via a local derivative operator. Although application of a model with derivative of more than second order improves the continuous model, a higher order of approximated differential equation seriously complicates a solution of continuous problem. It is known that accuracy of the approximation can dramatically increase using Padé approximations. In this paper, one- and two-point Padé approximations suitable for justify choice of structural damping models are used.
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44

Fitzpatrick, Patrick, and John Flynn. "A Gröbner basis technique for Padé approximation." Journal of Symbolic Computation 13, no. 2 (February 1992): 133–38. http://dx.doi.org/10.1016/s0747-7171(08)80087-9.

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45

Wang, Lei, and Yingui Sheng. "Fast bilateral filtering using the Padé approximation." Electronics Letters 53, no. 6 (March 2017): 395–97. http://dx.doi.org/10.1049/el.2017.0248.

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46

Graves-Morris, P. R., and D. E. Roberts. "Problems and progress in vector Padé approximation." Journal of Computational and Applied Mathematics 77, no. 1-2 (January 1997): 173–200. http://dx.doi.org/10.1016/s0377-0427(96)00127-6.

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47

Herceg, Dejana, Djordje Herceg, and Miroslav Prsa. "Using Padé Approximation in Takács Hysteresis Model." IEEE Transactions on Magnetics 51, no. 7 (July 2015): 1–4. http://dx.doi.org/10.1109/tmag.2015.2406299.

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48

Németh, G., and G. Páris. "The Gibbs phenomenon in generalized Padé approximation." Journal of Mathematical Physics 26, no. 6 (June 1985): 1175–78. http://dx.doi.org/10.1063/1.526521.

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49

González-Vera, P., and M. Jiménez Paiz. "Multipoint Padé-Type Approximation: An Algebraic Approach." Rocky Mountain Journal of Mathematics 29, no. 2 (June 1999): 531–58. http://dx.doi.org/10.1216/rmjm/1181071651.

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50

Fu, Bo-Ye, and Li-Yun Fu. "Poro-acoustoelastic constants based on Padé approximation." Journal of the Acoustical Society of America 142, no. 5 (November 2017): 2890–904. http://dx.doi.org/10.1121/1.5009459.

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