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Design and Implementation of Dolph Chebyshev and Zolotarev Circular Antenna Array

K. N. Mohan, D. Kannadassan, S. R. Zinka
2016 Indian Journal of Science and Technology  
Improvements: In comparison with uniformly excited UCAs, the Chebyshev and Zolotarev Polynomials show desirable radiation patterns with fewer elements.  ...  Along with phase modes, the magnitude distribution of elements is synthesized with Chebyshev and Zolotarev Polynomials whose resulting far-field patterns are desirable.  ...  The directional elements are excited with well-known Chebyshev and Zolotarev polynomials with even and odd numbers. The radius of CAA depends .  ... 
doi:10.17485/ijst/2016/v9i36/102137 fatcat:w5k3kf56kbhd7pxsgc5cd2e5xy

Compression of Ephemerides by Discrete Chebyshev Approximations

1979 Navigation  
The curve is typical of a discrete Chebyshev approximation.  ...  The table shows that a full period of the moon may be covered by Chebyshev polynomials of only degree 24 at a precision of 0 '035 in the angles and of 16 m in the distance (comparable to the accuracy maintained  ... 
doi:10.1002/j.2161-4296.1979.tb01350.x fatcat:dkipv7bqbbad3awpx4sbnyxg6u

Explicit Stabilized Runge–Kutta Methods [chapter]

Assyr Abdulle
2015 Encyclopedia of Applied and Computational Mathematics  
Synonyms Chebyshev methods, Runge-Kutta-Chebyshev methods Definition Explicit stabilized Runge-Kutta (RK) methods are explicit one-step methods with extended stability domains along the negative real axis  ...  RKC methods RKC methods rely on introducing a correction to the first order shifted Chebyshev polynomial to allow for second order polynomials.  ...  (11) where g 0 = y 0 , h i = γ i ∆t, γ i = −1/z i and z i are the zeros of the shifted Chebyshev polynomials.  ... 
doi:10.1007/978-3-540-70529-1_100 fatcat:uaqm2akvxnespazmwiemlljfz4

On the covering radius of an unrestricted code as a function of the rate and dual distance

Simon Litsyn, Patrick Solé, René Struik
1998 Discrete Applied Mathematics  
We present a uniform approach towards deriving upper bounds on the covering radius of a code as a function of its dual distance structure and its cardinality.  ...  Solt-and Stokes follow as special cases. Moreover, we obtain an asymptotic improvement of these bounds using Chebyshe\ polynomials. ZZ: . 0166-2lXX,'98!Sl9.00 0 1998 Elsevier Science B.V.  ...  Laihonen and A. Tietavainen for helpful discussions.  ... 
doi:10.1016/s0166-218x(97)00134-0 fatcat:hncw7nmbzbdtbovmztboe5ivea

The Eigenvalues of Second-Order Spectral Differentiation Matrices

J. A. C. Weideman, L. N. Trefethen
1988 SIAM Journal on Numerical Analysis  
By using the characteristic polynomial, a bound on the spectral radius of the differentiation matrix is derived that is accurate to 2% or better.  ...  In particular, it is proved that 7r points on average per wavelength are sufficient for successful interpolation of the eigenfunctions of the continuous operator in a Chebyshev distribution of nodes, and  ...  We gratefully acknowledge discussions with Daniele Funaro, David Gottlieb, and Manfred Trummer.  ... 
doi:10.1137/0725072 fatcat:7cko5whifjetras2lede4cob6q

Page 2405 of Mathematical Reviews Vol. , Issue 2000c [page]

2000 Mathematical Reviews  
The improvements of these bounds on the known results are based on the knowledge of the cardinality of constant weight codes and on the behavior of Hahn polynomials and discrete Chebyshev polynomials.”  ...  Discrete Math. 12 (1999), no. 2, 243-251 (electronic). Summary: “In this paper we estimate the covering radius when the dual distance is known. We derive new bounds on covering radii of linear codes.  ... 

On the tightness of Tietäväinen's bound for distributions with limited independence [article]

Louay Bazzi
2017 arXiv   pre-print
Namely, we show that there exists a k-wise independent probability distribution μ on {0,1}^n whose covering radius is at least n/2-√(kn).  ...  In 1990, Tietäväinen showed that if the only information we know about a linear code is its dual distance d, then its covering radius R is at most n/2-(1/2-o(1))√(dn).  ...  See [29] and [30] for a general reference on Chebyshev polynomials.  ... 
arXiv:1707.00552v1 fatcat:vr7mtolvtrclhoacxmosln33je

An efficient algorithm based on splitting for the time integration of the Schrödinger equation [article]

S. Blanes, F. Casas, A. Murua
2015 arXiv   pre-print
They can be considered, in this setting, as polynomial approximations to the matrix exponential in a similar way as methods based on Chebyshev and Taylor polynomials.  ...  The theoretical analysis, supported by numerical experiments, indicates that the new methods are more efficient than schemes based on Chebyshev polynomials for all tolerances and time intervals.  ...  AM is additionally partially supported by the Basque Government (Consolidated Research Group IT649-13), and FC by NPRP GRANT #5-674-1-114 from the Qatar National Research Fund.  ... 
arXiv:1502.06401v1 fatcat:u325qnde7je6lfoldhayr35qfi

A semi-infinite crack in front of a circular, thermally mismatched heterogeneity

W.H. Müller, H. Gao, C.-H. Chiu, S. Schmauder
1996 International Journal of Solids and Structures  
Gauss-Chebyshev, Lobatto-Chebyshev) as compared with those which cover the positive x-axis [0, co) (i.e. Radau-Chebyshev or Gauss-Hermite).  ...  It will be shown that among the discretizations for a finite interval the fastest to converge are those which explicitly use the end points -1 and + 1 (LobattoChebyshev) followed closely by polynomial  ...  l-t;2) N i= 1 (f-ii)(-l ' (38) where TN(i) is the Nth Chebyshev polynomial of the first kind.  ... 
doi:10.1016/0020-7683(95)00059-j fatcat:kxwpec337netnirvtied5gtqhq

Rarefied Poiseuille Flow in a Circular Tube

Oksana Germider, Vasily Popov, A. Nadykto, L. Uvarova, A. Zelensky, P. Pivkin, P. Lima, N. Aleksic, K. Egiazarian, X. Jiang
2019 EPJ Web of Conferences  
This approach is based on the Chebyshev polynomials and rational Chebyshev functions.  ...  Based on the proposed approach, we have calculated the mass and the heat fluxes through the tube. The obtained results have also been compared with other studies.  ...  Solution to the problem The function ( , , ) Z C ⊥ ρ ζ defined on [0,1] [ 1,1] [0, ) × − × ∞ may be expanded in the Chebyshev polynomials 1 * { ( )} j T ρ , 2 { ( )} j T ζ and the rational Chebyshev functions  ... 
doi:10.1051/epjconf/201922402001 fatcat:hpuubpmjevabzas2mw46eeje6y

Residual-Minimizing Krylov Subspace Methods for Stabilized Discretizations of Convection-Diffusion Equations

Oliver G. Ernst
2000 SIAM Journal on Matrix Analysis and Applications  
We discuss the behavior of the minimal residual method applied to stabilized discretizations of one-and two-dimensional model problems for the stationary convectiondi usion equation.  ...  In the two-dimensional model problem considered, we observe two distinct phases in the convergence of the iterative method: the rst determined by the eld of values and the second by the spectrum.  ...  1; 1], the rst-kind Chebyshev polynomials can be de ned by from which we conclude that the m-th Chebyshev polynomial maps the ellipse E to the ellipse E m, which is covered m times.  ... 
doi:10.1137/s0895479897325761 fatcat:gpgq7kzi3rawtm5ebmzujt72vy

On the orthogonality of the Chebyshev-Frolov lattice and applications [article]

Christopher Kacwin, Jens Oettershagen, Tino Ullrich
2016 arXiv   pre-print
We deal with lattices that are generated by the Vandermonde matrices associated to the roots of Chebyshev-polynomials.  ...  We prove that the resulting lattices are orthogonal and possess a lattice representation matrix with entries not larger than 2 (in modulus).  ...  Temlyakov and M. Ullrich on the topic of this paper. Tino Ullrich gratefully acknowledges support by the German Research Foundation (DFG) and the Emmy-Noether programme, Ul-403/1-1.  ... 
arXiv:1606.00492v2 fatcat:jeoswbzfwzaabje5t4ilfntxcu

Local Fourier Analysis of Multigrid Methods with Polynomial Smoothers and Aggressive coarsening [article]

James Brannick, Xiaozhe Hu, Carmen Rodrigo, Ludmil Zikatanov
2014 arXiv   pre-print
We focus on the study of multigrid methods with aggressive coarsening and polynomial smoothers for the solution of the linear systems corresponding to finite difference/element discretizations of the Laplace  ...  The methods we introduce are highly parallelizable and efficient multigrid algorithms on structured and semi-structured grids in two and three spatial dimensions.  ...  Carmen Rodrigo gratefully acknowledges the hospitality of the Center for Computational Mathematics and Applications and  ... 
arXiv:1310.8385v2 fatcat:mgh4gkcxfjf7papetuka7d5odm

Convergence properties of the Runge-Kutta-Chebyshev method

J. G. Verwer, W. H. Hundsdorfer, B. P. Sommeijer
1990 Numerische Mathematik  
The Runge-Kutta-Chebyshev method is ans-stage Runge-Kutta method designed for the explicit integration of stiff systems of ordinary differential equations originating from spatial discretization of parabolic  ...  Internal stability has to do with the propagation of errors over the stages within one single integration step.  ...  We thank Ernst Hairer for bringing the article by Guillou and Lago [3] to our notice.  ... 
doi:10.1007/bf01386405 fatcat:uknsccf5xrf67lhhsy32eyxh3y

Chebyshev collocation method and multi-domain decomposition for Navier-Stokes equations in complex curved geometries

C.R. Schneidesch, M.O. Deville
1993 Journal of Computational Physics  
Spatial discretization proceeds by covering the physical domain B with a discrete Chebyshev mesh %N which coincides with the domain at the boundaries.  ...  Thus, one may write where Tkxi denotes the first-order derivative of the Chebyshev polynomial of the first kind and degree NXi.  ... 
doi:10.1016/s0021-9991(83)71105-8 fatcat:zvefywoh25bkdpqfqkfhywq6o4
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