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Chebyshev expansions and rational approximations

Yudell L. Luke
1976 Journal of Computational and Applied Mathematics  
Suppose that for each representation there is a sequence of rational approximations of the same type, say of the Pad6 class, which converge for larg z l < ,r except possibly for some finite set of points  ...  A variant of this problem is the situation where A(z) and B(z,m) are approximated by their representations in infinite series of Chebyshev polynomials of the first kind truncated after n and r terms respectively  ...  As in the [' (v, z) analysis, we now consider the relative merits of the Pad~ approximation of order n and the truncated Chebyshev expansion of m terms.  ... 
doi:10.1016/0771-050x(76)90013-9 fatcat:37qmvxfyabeevcr5nonavxapua

Wide‐angle one‐way wave equations

Laurence Halpern, Lloyd N. Trefethen
1988 Journal of the Acoustical Society of America  
The design of a one-way wave equation is connected with the approximation of ( 1 --s •) J t2 on [ --1,1 ] by a rational function, which has usually been carried out by Pad6 approximation.  ...  This article presents coefficients for L 2, L •, and other alternative classes of approximants that have better wide-angle behavior.  ...  We computed coefficients of Chebyshev-Padapproximations by a standard procedure due to Gragg?  ... 
doi:10.1121/1.396586 pmid:3198873 fatcat:lvr7jjwrxvhwhkigzcoaujcgyu

The Parallel One-way Hash Function Based on Chebyshev-Halley Methods with Variable Parameter

Mahdi Nouri, Mahyar Safarinia, Payam Pourmahdi, Mohammad Hossein Garshasebi
2014 International Journal of Computers Communications & Control  
Theoretical analysis and computer simulation indicate that the algorithm can assure all performance requirements of hash function in an efficient and flexible style and secure against birthday attacks  ...  In this paper a parallel Hash algorithm construction based on the Chebyshev Halley methods with variable parameters is proposed and analyzed.  ...  Pad as follows: if 12 ≤ d < 16 then pad 12d bytes, otherwise pad 28d bytes, the bytes been padded come from the head of message. The last four bytes are padded with message length.  ... 
doi:10.15837/ijccc.2014.1.867 fatcat:jwadcl22ijbr7a3chsgricocfe

Bivariate Lagrange interpolation at the Padua points: Computational aspects

Marco Caliari, Stefano De Marchi, Marco Vianello
2008 Journal of Computational and Applied Mathematics  
Moreover, the associated Lebesgue constant has minimal order of growth O(log 2 (n)).  ...  Here we show four families of Padua points for interpolation at any even or odd degree n, and we present a stable and efficient implementation of the corresponding Lagrange interpolation formula, based  ...  Another useful feature of the Fourier-Chebyshev representation is the possibility of estimating a posteriori the interpolation error by the size of some coefficients, as we shall see below.  ... 
doi:10.1016/j.cam.2007.10.027 fatcat:mcjhyxwrlfgqpfvu4jlqwxxgdi

Page 3246 of Mathematical Reviews Vol. , Issue 83h [page]

1983 Mathematical Reviews  
K. 83h:41019 Gonevalieations of Pads apgrexiseation for Chebyshev and Fourier series. E. B. Christoffel ( Aachen / Monschau, 1979), pp. 212-231, Birkhauser, Basel, 1981.  ...  s3n:4 1 o16 to characterize some essential property of D, or more generally, can some class of operators be identified in terms of this “natural” property of the d‘?  ... 

A comparison of numerical and analytical methods for the reduced wave equation with multiple spatial scales

John P. Boyd
1991 Applied Numerical Mathematics  
., A comparison of numerical and analytical methods for the reduced wave equation with multiple spatial scales, Applied Numerical Mathematics 7 (1991) 453-479.  ...  This indeterminancy can only be resolved by the needs of the physical analysis. Lorenz for some constants a( E) and fi( E).  ...  The numerical evidence suggests that Pad& approximants-or at least some subsequencesconverge for Case 1 (exponentially decaying solutions).  ... 
doi:10.1016/0168-9274(91)90038-2 fatcat:tbbg76yssjcp7ftzocju4e2v34

Solution of second order difference equations via the τ-method

Yudell L. Luke
1981 Computers and Mathematics with Applications  
Ah&ad-Classically the solution of many functional equations is sought in the form of an intinite series of some kind. In practice, to get numerical results, the series must be truncated.  ...  Except for some recent work on the gamma function by the author, Wimp and Ting, the literature is void on use of the r-method idea for solutions of diicrencc equations.  ...  Acknowledgement-It is a pleasure to acknowledge with thanks the expert assistance of Dr. Bing Y. Ting.  ... 
doi:10.1016/0898-1221(81)90131-0 fatcat:2h4hislrirdljc23ah37oq65qy

Dzydyk's research on the theory of approximation of functions of a complex variable

V. I. Belyi, A. P. Golub, I. A. Shevchuk
1989 Ukrainian Mathematical Journal  
Dzydyk's studies in the area of mathematical analysis and its applications are well known to a broad group of specialists.  ...  , Pade approximation, and the problem of moments, and also strengthened several classical results.  ...  in the theory of Pad~ approximation.  ... 
doi:10.1007/bf01060614 fatcat:bwk3ggztoncjpoljwwmrrrwwxu

Fractality of metal pad instability threshold in rectangular cells [article]

Gerasimos Politis, Jānis Priede
2021 arXiv   pre-print
rotating interfacial wave which is known as the metal pad instability.  ...  We analyse linear stability of interfacial waves in an idealised model of an aluminium reduction cell consisting of two stably stratified liquid layers which carry a vertical electric current in a collinear  ...  Section §3 presents linear stability analysis of rectangular cells which is carried out analytically using an eigenvalue perturbation method as well as numerically using the Galerkin and the Chebyshev  ... 
arXiv:2002.09975v3 fatcat:v3l5xttgwzgqhgc3fmfre2lue4

Nonlinear viscoelastic biomaterials: meaningful characterization and engineering inspiration

R. H. Ewoldt, A. E. Hosoi, G. H. McKinley
2009 Integrative and Comparative Biology  
We have developed data-analysis software to enable wider use of this framework within and beyond the biomaterials community. The functionality of this software is outlined here. 1  ...  We discuss the progress made toward bioinspired snail-like locomotion and the pursuit of an engineered fluid that imitates the nonlinear viscoelastic properties of native gastropod pedal mucus.  ...  Biochemistry (DCPB), SICB Division of Vertebrate Morphology (DVM), Air Force Office of Scientific Research (AFOSR), National Science Foundation (NSF), and the journal Zoology.  ... 
doi:10.1093/icb/icp010 pmid:21669845 fatcat:6xjenbfegrcjhbbubsy2or6t2u

Cosmographic analysis with Chebyshev polynomials

Salvatore Capozziello, Rocco D'Agostino, Orlando Luongo
2018 Monthly notices of the Royal Astronomical Society  
In addition, we theoretically evaluate the convergence radius of (1,1) Chebyshev rational polynomial and we compare it with the convergence radii of Taylor and Pad\'e approximations.  ...  To figure this out, we compare rational Chebyshev polynomials with Pad\'e series.  ...  S.C. acknowledges the support of INFN (iniziativa specifica QGSKY). R.D. thanks Federico Tosone for useful discussions on the Monte Python code.  ... 
doi:10.1093/mnras/sty422 fatcat:ixfpexr5lbg6jf3j3wc5kn5hyq

On the parallel solution of parabolic equations

E. Gallopoulos, Y. Saad
1989 Proceedings of the 3rd international conference on Supercomputing - ICS '89  
The two other methods proposed are based on Padk and Chebyshev approximations to the matrix exponential.  ...  We propose new parallel algorithms for the solution of linear parabolic problems. The first of these methods is based on using polynomial approximation to the exponential.  ...  The research of the second author was supported by NASA under USRA Grant No. NCC 2-387.  ... 
doi:10.1145/318789.318793 dblp:conf/ics/GallopoulosS89 fatcat:lz3fm3rydffo5m7pprzkat77py

Method to Design UF-OFDM Filter and its Analysis [article]

Hirofumi Tsuda, Ken Umeno
2017 arXiv   pre-print
Our filters have smaller side-lobes and lower Bit Error Rate than the Dolph-Chebyshev filter.  ...  One of them is that OFDM signals have high Peak-to-Average Power Ratio (PAPR). The other problem is that OFDM signals have large side-lobes.  ...  Acknowledgment The one of the authors, Hirofumi Tsuda, would like to thank Dr. Shin-itiro Goto for his advise.  ... 
arXiv:1711.07197v1 fatcat:boqda3ozy5bkffzjuape6plf6y

Fast Approximate Fourier Transforms for Irregularly Spaced Data

Antony F. Ware
1998 SIAM Review  
The algorithms can be viewed as approximate generalizations of the fast Fourier transform (FFT), and they are compared with regard to their accuracy and their computational efficiency.  ...  In this case the approximation is based on a projection onto a subspace of a multiresolution analysis.  ...  Some methods of choosing an appropriate value for b, and the effect of varying b on the accuracy of the approximation, will be discussed below. 2.4.1. Approximation properties.  ... 
doi:10.1137/s003614459731533x fatcat:gx32rtt4undupipd7hezi65bay

Preface

N. Papamichael, E.B. Saff
1993 Journal of Computational and Applied Mathematics  
They also discuss possible applications in connection with Pad&type approximation and Gaussian quadrature methods.  ...  This special issue is devoted to Computational Complex Analysis, i.e., to topics dealing with various computational aspects of complex analysis such as approximation and quadrature in the complex plane  ... 
doi:10.1016/0377-0427(93)90283-h fatcat:oczjyl3gnjf37lgzychzqvzazu
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