共查询到20条相似文献,搜索用时 9 毫秒
1.
The Legendre rational approximation is investigated. Some approximation results are established, which form the mathematical foundation of a new spectral method on the whole line. A model problem is considered. Numerical results show the efficiency of this new approach. 相似文献
2.
Zhong-Qing Wang 《Journal of Mathematical Analysis and Applications》2002,274(1):374-403
An orthogonal system of rational functions is discussed. Some inverse inequalities, imbedding inequalities and approximation results are obtained. Two model problems are considered. The stabilities and convergences of proposed rational spectral schemes and rational pseudospectral schemes are proved. The techniques used in this paper are also applicable to other problems on the whole line. Numerical results show the efficiency of this approach. 相似文献
3.
Shan Li Qiao-ling Li Zhong-qing Wang 《Mathematical Methods in the Applied Sciences》2020,43(1):255-268
Modified Legendre rational spectral methods for solving second-order differential equations on the half line are proposed. Some Sobolev orthogonal Legendre rational basis functions are constructed, which lead to the diagonalization of discrete systems. Accordingly, both the exact solutions and the approximate solutions can be represented as infinite and truncated Fourier series. Numerical results demonstrate the effectiveness and the spectral accuracy of this approach. 相似文献
4.
V. N. Rusak 《Mathematical Notes》1977,22(3):699-702
For a given system of numbers {z
k
}
k=1
n
, IMz
k
> 0, rational functions of order 4n — 2 are constructed which effect for a functionf(x∈C
∞) an approximation of the same order as the best approximation by proper rational functions having poles at the points {z
k
k=1
n
and
.
Translated from Matematicheskie Zametki, Vol. 22, No. 3, pp. 375–380, September, 1977.
In conclusion the author thanks E. P. Dolzhenko and S. B. Stechkin, whose discussions contributed to improvements in this
work. 相似文献
5.
We compute the Hausdorff dimension of sets of very well approximable vectors on rational quadrics. We use ubiquitous systems
and the geometry of locally symmetric spaces. As a byproduct we obtain the Hausdorff dimension of the set of rays with a fixed
maximal singular direction, which move away into one end of a locally symmetric space at linear depth, infinitely many times. 相似文献
6.
7.
Charles B. Dunham 《BIT Numerical Mathematics》1982,22(1):119-122
Chebyshev approximation on an interval [, ] by ordinary rational functions when positive deviations (errors) are magnified by a bias factor is considered. This problem is related to one-sided Chebyshev approximation for large bias factors. Best approximations are characterized by alternation. Non-degenerate best approximations can be determined by the Remez algorithm. A variant of the Fraser-Hart-Remez algorithm is implemented. 相似文献
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11.
12.
Marc Van Barel Adhemar Bultheel 《Journal of Computational and Applied Mathematics》1994,50(1-3):545-563
We already generalized the Rutishauser—Gragg—Harrod—Reichel algorithm for discrete least-squares polynomial approximation on the real axis to the rational case. In this paper, a new method for discrete least-squares linearized rational approximation on the unit circle is presented. It generalizes the algorithms of Reichel—Ammar—Gragg for discrete least-squares polynomial approximation on the unit circle to the rationale case. The algorithm is fast in the sense that it requires order m computation time where m is the number of data points and is the degree of the approximant. We describe how this algorithm can be implemented in parallel. Examples illustrate the numerical behavior of the algorithm. 相似文献
13.
We obtain a characterization for Lp approximation by analytic functions on compact plane sets which is analogous to Vitushkin's characterization for uniform approximation. For p = 2 this was done by Havin by use of Cartan's fine topology; we study the general case by use of quasi topologies. 相似文献
14.
G. Németh 《Mathematical Notes》1977,21(4):325-328
15.
16.
《Journal de Mathématiques Pures et Appliquées》1999,78(2):177-202
Given a triple (G, W, γ) of an open bounded set G in the complex plane, a weight function W(z) which is analytic and different from zero in G, and a number γ with 0 ≤ γ ≤ 1, we consider the problem of locally uniform rational approximation of any function ƒ(z), which is analytic in G, by weighted rational functions Wmi+ni(z)Rmi, ni(z)i = 0∞, where Rmi, ni(z) = Pmi(z)/Qni(z) with deg Pmi ≤ mi and deg Qni ≤ ni for all i ≥ 0 and where mi + ni → ∞ as i → ∞ such that lim mi/[mi + ni] = γ. Our main result is a necessary and sufficient condition for such an approximation to be valid. Applications of the result to various classical weights are also included. 相似文献
17.
We consider rational approximations of the form
相似文献
18.
使用勒让德正交多项式逼近方法,将Lagrange型最优控制问题转化为非线性规划问题.采用序列二次规划方法对此非线性规划问题的求解,并对多项式逼近和非线性规划求解后得到的解是否收敛给出了证明和实例分析. 相似文献
19.
H. -P. Blatt 《Ukrainian Mathematical Journal》2006,58(1):1-11
The error curve for the rational best approximation of ƒ ∈ C[−1, 1] is characterized by the well-known equioscillation property. Contrary to the polynomial case, the distribution of
these alternations is not governed by the equilibrium distribution. It is known that these points need not be dense in [−1,
1]. The reason is the influence of the distribution of the poles of rational approximants. In this paper, we generalize the
results known so far to situations where the requirements for the degrees of numerators and denominators are less restrictive.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 1, pp. 3–11, January, 2006. 相似文献
20.
We show that the Hurwitz zeta function, , and the Legendre chi function, , defined by
and respectively, form a discrete Fourier transform pair. Many formulae involving the values of these functions at rational arguments, most of them unknown, are obtained as a corollary to this result. Among them is the further simplification of the summation formulae from our earlier work on closed form summation of some trigonometric series for rational arguments. Also, these transform relations make it likely that other results can be easily recovered and unified in a more general context. |