Hermitian Finite Element Complementing the Bogner–Fox–Schmit Rectangle Near Curvilinear Boundary

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Numerical Probabilistic Approach for Optimization Problems

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Numerical Probabilistic Approach for Optimization Problems

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Piecewise Polynomial Aggregation as Preprocessing for Data Numerical Modeling

Abstract. Data aggregation issues for numerical modeling are reviewed in the present study. The authors discuss data aggregation procedures as preprocessing for subsequent numerical modeling. To calculate the data aggregation, the authors propose using numerical probabilistic analysis (NPA). An important feature of this study is how the authors represent the aggregated data. The study shows that the offered approach to data aggregation can be interpreted as the frequency distribution of a variable. To study its properties, the density function is used. For this purpose, the authors propose using the piecewise polynomial models. A suitable example of such approach is the spline. The authors show that their approach to data aggregation allows reducing the level of data uncertainty and significantly increasing the efficiency of numerical calculations. To demonstrate the degree of the correspondence of the proposed methods to reality, the authors developed a theoretical framework and considered numerical examples devoted to time series aggregation

Hermitian Finite Element Complementing the Bogner–Fox–Schmit Rectangle Near Curvilinear Boundary

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Piecewise Polynomial Aggregation as Preprocessing for Data Numerical Modeling

Data aggregation issues for numerical modeling are reviewed in the present study. The authors discuss data aggregation procedures as preprocessing for subsequent numerical modeling. To calculate the data aggregation, the authors propose using numerical probabilistic analysis (NPA). An important feature of this study is how the authors represent the aggregated data. The study shows that the offered approach to data aggregation can be interpreted as the frequency distribution of a variable. To study its properties, the density function is used. For this purpose, the authors propose using the piecewise polynomial models. A suitable example of such approach is the spline. The authors show that their approach to data aggregation allows reducing the level of data uncertainty and significantly increasing the efficiency of numerical calculations. To demonstrate the degree of the correspondence of the proposed methods to reality, the authors developed a theoretical framework and considered numerical examples devoted to time series aggregatio

Ground state of a periodic elastic atomic chain in an arbitrary periodic potential

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The ground state of the Frenkel–Kontorova model

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The ground state of the Frenkel–Kontorova model

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