scholarly journals An Estimate of the Rate of Convergence of the Fourier Series in the Generalized Hölder Metric by Delayed Arithmetic Mean

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
L. Nayak ◽  
G. Das ◽  
B. K. Ray
Keyword(s):  
Fourier Series ◽  
Rate Of Convergence ◽  
Arithmetic Mean ◽  
Convergence Problem ◽  
Hölder Metric ◽  
Generalized Hölder Metric

We study the rate of convergence problem of the Fourier series by Delayed Arithmetic Mean in the generalized Hölder metric (Hp(w)) space which was earlier introduced by Das, Nath, and Ray and obtain a sharper estimate of Jackson's order.

On approximation of the rate of convergence of Fourier series in the generalized Hölder metric by Deferred Nörlund mean

2019 ◽  
Vol 30 (7-8) ◽  
pp. 1119-1131 ◽  
Author(s):  
T. Pradhan ◽  
B. B. Jena ◽  
S. K. Paikray ◽  
H. Dutta ◽  
U. K. Misra
Keyword(s):  
Fourier Series ◽  
Rate Of Convergence ◽  
Hölder Metric ◽  
Generalized Hölder Metric

DEPENDENCE OF THE QUALITY OF MACHINE TRANSLATION OF THE TEXT ON THE USED FOURIER TRANSFORMATION

2021 ◽  
Vol 4 ◽  
pp. 69-80
Author(s):  
Valentin Sobchuk ◽  
◽  
Galina Kharkevych ◽  
Keyword(s):  
Fourier Series ◽  
Rate Of Convergence ◽  
Machine Translation ◽  
Fourier Transformation ◽  
Scientific Information ◽  
Necessary Condition ◽  
Linear Matrix ◽  
Matrix Methods ◽  
Filtering Algorithms ◽  
Fourier Filtering

Machine translation is widely used in the translation of commercial, technical, scientific information that is connected with the process of globalization and, accordingly, the expansion of the network of business relations. Mathematical methods related to machine translation of the texts have recently received new development due to the intensive development of Fourier transformation theory. Thus, the requirements for filtering accuracy in the processing of contrast signals and images have increased, allowing to create efficient filtering algorithms. Frequency algorithms are the most efficient of all the existing filtering algorithms, i.e., those where the coefficients of decomposition of the noisy signal by Fourier basis are the subject to processing. When using Fourier filtering algorithms, the properties of Fourier transformation play an important role, that depend on belonging to a particular class of differential functions. The necessary condition for the existence of the continuous Fourier transformation is the absolute convergence of some functions by means of which the real studied process is describing. In practice, the so-called “summation functions” are often used as simulated functions, which can be constructed using a linear matrix summation of Fourier series. As for the latter, scientists distinguish between both triangular and rectangular linear matrix methods. This paper is devoted to the study of the convergence conditions of Fourier transformations of both triangular and rectangular linear matrix methods for summing Fourier series. Moreover, this article shows that the rate of convergence of Fourier transformation of the rectangular linear Abel-Poisson method is at times faster than the rate of convergence of the analogous triangular linear Abel-Poisson method. This result can further significantly influence the choice of the more effective Fourier transformation used in the process of machine translation of the text.

Sign in / Sign up

Export Citation Format

Share Document