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Design and Implementation of Dolph Chebyshev and Zolotarev Circular Antenna Array
2016
Indian Journal of Science and Technology
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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
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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]
2015
Encyclopedia of Applied and Computational Mathematics
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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
1998
Discrete Applied Mathematics
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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
1988
SIAM Journal on Numerical Analysis
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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
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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]
2017
arXiv
pre-print
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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]
2015
arXiv
pre-print
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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
1996
International Journal of Solids and Structures
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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
2019
EPJ Web of Conferences
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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
2000
SIAM Journal on Matrix Analysis and Applications
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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]
2016
arXiv
pre-print
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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]
2014
arXiv
pre-print
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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
1990
Numerische Mathematik
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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
1993
Journal of Computational Physics
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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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