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1.
S. Tikhonov 《Journal of Mathematical Analysis and Applications》2007,326(1):721-735
We study trigonometric series with general monotone coefficients. Convergence results in the different metrics are obtained. Also, we prove a Hardy-type result on the behavior of the series near the origin. 相似文献
2.
Let μ be a finite positive Borel measure supported in [−1,1] and introduce the discrete Sobolev-type inner productwhere the mass points ak belong to [−1,1], Mk,i0, i=0,…,Nk−1, and Mk,Nk>0. In this paper, we study the asymptotics of the Sobolev orthogonal polynomials by comparison with the orthogonal polynomials with respect to the measure μ and we prove that they have the same asymptotic behaviour. We also study the pointwise convergence of the Fourier series associated to this inner product provided that μ is the Jacobi measure. We generalize the work done by F. Marcellán and W. Van Assche where they studied the asymptotics for only one mass point in [−1,1]. The same problem with a finite number of mass points off [−1,1] was solved by G. López, F. Marcellán and W. Van Assche in a more general setting: they consider the constants Mk,i to be complex numbers. As regards the Fourier series, we continue the results achieved by F. Marcellán, B. Osilenker and I.A. Rocha for the Jacobi measure and mass points in
. 相似文献
3.
A numerical computation in crystallography involves an infinite integral depending on one parameter. In a recent article in this journal this computational problem is addressed using Romberg’s method and tools for error control. One observe numerical difficulties with the reported approach both near the parameter’s endpoints and near the parameter interval’s midpoint. In this short note we will present an alternative approach making use of a known infinite series formulation of the problem at hand and a simple and efficient series acceleration technique. If some care is taken to avoid cancellations the numerical results are excellent for all values of the parameter.
AMS subject classification 65B05, 65B10, 65D30 相似文献
4.
We discuss the effect of a particular sequence acceleration method, the Lubkin W-transform, on the partial sums of Fourier
series. We consider a very general class of functions with a single jump discontinuity, and prove that this method fails on
a large set of points.
The authors were partially supported by the Kansas State University REU and NSF grant GOMT530725. 相似文献
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6.
André Draux 《Numerical Algorithms》1996,11(1):143-158
From some results concerning the formal orthogonal polynomials, already proved in [5], we develop new properties of generalized adjacent polynomials which correspond to a change in the weight function. A new structure of the singular blocks is given. These results have a direct application to Lanczos methods, theG and -algorithms. 相似文献
7.
Pawe? Wo?ny 《Applied mathematics and computation》2009,215(4):1622-1645
A new method of summation of slowly convergent series is proposed. It may be successfully applied to the summation of generalized and basic hypergeometric series, as well as some classical orthogonal polynomial series expansions. In some special cases, our algorithm is equivalent to Wynn’s epsilon algorithm, Weniger transformation [E.J. Weniger, Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series, Computer Physics Reports 10 (1989) 189-371] or the technique recently introduced by ?í?ek et al. [J. ?í?ek, J. Zamastil, L. Skála, New summation technique for rapidly divergent perturbation series. Hydrogen atom in magnetic field, Journal of Mathematical Physics 44 (3) (2003) 962-968]. In the case of trigonometric series, our method is very similar to the Homeier’s H transformation, while in the case of orthogonal series — to the K transformation. Two iterated methods related to the proposed method are considered. Some theoretical results and several illustrative numerical examples are given. 相似文献
8.
A series is called a pointwise universal trigonometric series if for any , there exists a strictly increasing sequence of positive integers such that converges to f(z) pointwise on . We find growth conditions on coefficients allowing and forbidding the existence of a pointwise universal trigonometric series. For instance, if as |n|→∞ for some ε>0, then the series Sa cannot be pointwise universal. On the other hand, there exists a pointwise universal trigonometric series Sa with as |n|→∞. 相似文献
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Arnak Poghosyan 《分析论及其应用》2010,26(3):236-260
Convergence acceleration of the classical trigonometric interpolation by the Eckhoff method is considered, where the exact values of the jumps are approximated by solution of a system of linear equations. The accuracy of the jump approximation is explored and the corresponding asymptotic error of interpolation is derived. Numerical results validate theoretical estimates. 相似文献
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Thomas Dehn 《Journal of Computational and Applied Mathematics》1994,50(1-3):207-219
We consider the asymptotic behavior of the ratios qn+1(z)/qn(z) of polynomials orthonormal with respect to some positive measure μ. Let the recurrence coefficients n and βn converge to 0 and
, respectively. Then, qn+1(z)/qn(z) Φ(z),for n→∞ locally uniformly for
, where Φ maps
conformally onto the exterior of the unit disc (Nevai (1979)). We provide a new and direct proof for this and some related results due to Nevai, and apply it to convergence acceleration of diagonal Padé approximants. 相似文献
14.
R. Álvarez-Nodarse R.S. Costas-Santos 《Journal of Mathematical Analysis and Applications》2006,322(1):158-176
In this paper, we consider a natural extension of several results related to Krall-type polynomials introducing a modification of a q-classical linear functional via the addition of one or two mass points. The limit relations between the q-Krall type modification of big q-Jacobi, little q-Jacobi, big q-Laguerre, and other families of the q-Hahn tableau are established. 相似文献
15.
J. Marshall Ash Sh. T. Tetunashvili 《Proceedings of the American Mathematical Society》2000,128(9):2627-2636
A uniqueness theorem is proved for trigonometric series and another one is proved for multiple trigonometric series. A corollary of the second theorem asserts that there are two subsets of the -dimensional torus, the first having a countable number of points and the second having points such that whenever a multiple trigonometric series ``converges' to zero at each point of the former set and also converges absolutely at each point of the latter set, then that series must have every coefficient equal to zero. This result remains true if ``converges' is interpreted as any of the usual modes of convergence, for example as ``square converges' or as ``spherically converges.'
16.
Numerical Algorithms - We propose a new simple convergence acceleration method for a wide range class of convergent alternating series. It has some common features with Smith’s and... 相似文献
17.
E.X.L. de Andrade 《Journal of Mathematical Analysis and Applications》2007,330(1):114-132
We consider a connection that exists between orthogonal polynomials associated with positive measures on the real line and orthogonal Laurent polynomials associated with strong measures of the class S3[0,β,b]. Examples are given to illustrate the main contribution in this paper. 相似文献
18.
The main aim of this paper is to prove that the logarithmic means of quadratical partial sums of the double Walsh-Fourier series does not improve the convergence in measure. In other words, we prove that for any Orlicz space, which is not a subspace of LlnL(I2), the set of the functions having logarithmic means of quadratical partial sums of the double Walsh-Fourier series convergent in measure is of first Baire category. 相似文献
19.
Dimitar K. Dimitrov Francisco Marcellán 《Journal of Mathematical Analysis and Applications》2010,368(1):80-89
Denote by , k=1,…,n, the zeros of the Laguerre-Sobolev-type polynomials orthogonal with respect to the inner product
20.
Alphonse P. Magnus Viviane Pierrard 《Journal of Computational and Applied Mathematics》2008,219(2):431
One considers the recurrence relation of orthogonal polynomials related to weights |t|A(1+t2r/c2r)-B on the whole real line, for various integer exponents 2r, and real A>-1, B>0. 相似文献