Many-Dimensional Generalized Moment Representations and Padé -Type Approximants for Functions of Many Variables

Holub, A. P.; Chernets’ka, L. O.

doi:10.1007/s11253-015-1010-7

Cited by 2 publications

(4 citation statements)

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“…Lately, there has been a significant focus on extending the classical theory of approximation using fractional-rational functions. This includes exploring different types of basis functions and various methods of constructing approximants, such as Padé-type approximations [12,[14][15][16][17][18][19]. By carefully selecting the construction method, significant enhancements in the desirable properties of the approximants can be achieved for specific classes of functions [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Raster image processing using 2D Padé-type approximations

Olevskyi,

Olevska,

Olevskyi

et al. 2023

J. Phys.: Conf. Ser.

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We have developed a method called the two-dimensional Padé-type approximants method, which can be used to reduce the Gibbs phenomenon in the harmonic two-dimensional Fourier series. This method can be applied to both monochrome and color raster images. To do this, we implement the generalized two-dimensional Padé approximation proposed by Chisholm. In this approach, we select the range of frequency values on the integer grid according to the Vavilov method. We propose a definition of a Padé-type functional and provide examples of its application to simple discontinuous templates represented as raster images. Through this study, we are able to draw conclusions about the practical usage and advantages of the Padé-type approximation. We demonstrate that the Padé-type approximant effectively eliminates distortions associated with the Gibbs phenomenon, and it is visually more appropriate than the Fourier approximant. Additionally, the application of the Padé-type approximation reduces the number of parameters without sacrificing precision.

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Section: Introductionmentioning

confidence: 99%

Raster image processing using 2D Padé-type approximations

Olevskyi,

Olevska,

Olevskyi

et al. 2023

J. Phys.: Conf. Ser.

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“…Later, the method of generalized moment representations was developed for two-and multidimensional sequences [5,6]. This led to the problem of determination of the conditions of existence of generalized multidimensional moment representations.…”

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confidence: 99%

“…Definition 3 [6]. A generalized moment representation of a d-dimensional number sequence {s k } k2Z d + on the product of linear spaces X ⇥ Y is defined as a collection of equalities…”

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confidence: 99%