Padé -Type Approximants for Some Classes of Multivariate Functions

Holub, A. P.; Lysenko, L. O.

doi:10.1007/s11253-017-1391-x

Cited by 2 publications

(2 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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“…Approximation by rational fractions has a number of advantages over other types of approximation [5,6]. In particular, rational fractions can provide:…”

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confidence: 99%

An Ensemble Method for the Regression Model Parameter Adjustments: Direct Approach

Izonin

2023

mcm-tech

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Intelligence analysis of tabular datasets in the field of biomedical engineering is a complex task. This is explained both by the multidimensional datasets and the complex relationships between the components of the set, and by the high price of the error in the prediction. The task becomes more difficult in the case of limited data for training, which often occurs in this field. This is due to the enormous time, material, or human resources required to collect enough data to implement training procedures with classical machine learning tools. This paper presents a new approach to solving this task. The author has developed a new ensemble method for the regression model parameters adjustments (direct approach) with the possibility of cyclically increasing the accuracy of intellectual analysis of short datasets. The basis of the method is the use of the rational fraction and two machine learning algorithms for its parametric identification. Modeling of the method's efficiency on a real-world short set of data from the field of biomedical engineering demonstrated the high accuracy of the developed method's operation. In particular, the prediction accuracy of the General Regression Neural Network was increased by more than 14% (based on the coefficient of determination. That is why the developed method can be used to solve various applied biomedical engineering tasks in the case of the need to analyze small amounts of data

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Padé -Type Approximants for Some Classes of Multivariate Functions

Cited by 2 publications

References 1 publication

Raster image processing using 2D Padé-type approximations

Raster image processing using 2D Padé-type approximations

An Ensemble Method for the Regression Model Parameter Adjustments: Direct Approach

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