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    Wyświetlanie 1-8 z 8
    Tytuł:
    Newtons iteration with a conjugate gradient based decomposition method for an elliptic PDE with a nonlinear boundary condition
    Autorzy:
    Koko, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/907312.pdf
    Data publikacji:
    2004
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    metoda Newtona
    metoda gradientu sprzężonego
    warunek brzegowy nieliniowy
    Newton's method
    conjugate gradient method
    nonlinear PDE
    Opis:
    Newton's iteration is studied for the numerical solution of an elliptic PDE with nonlinear boundary conditions. At each iteration of Newton's method, a conjugate gradient based decomposition method is applied to the matrix of the linearized system. The decomposition is such that all the remaining linear systems have the same constant matrix. Numerical results confirm the savings with respect to the computational cost, compared with the classical Newton method with factorization at each step.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2004, 14, 1; 13-18
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analytical solution of the time fractional Fokker-Planck equation
    Autorzy:
    Sutradhar, T.
    Datta, B. K.
    Bera, R. K.
    Powiązania:
    https://bibliotekanauki.pl/articles/955129.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    równanie Fokkera-Plancka
    równania różniczkowe
    mechanika stosowana
    Fokker-Planck equation
    Adomian decomposition method
    fractional calculus
    fractional differential equation
    Opis:
    A nonperturbative approximate analytic solution is derived for the time fractional Fokker-Planck (F-P) equation by using Adomian’s Decomposition Method (ADM). The solution is expressed in terms of Mittag-Leffler function. The present method performs extremely well in terms of accuracy, efficiency and simplicity.
    Źródło:
    International Journal of Applied Mechanics and Engineering; 2014, 19, 2; 435-440
    1734-4492
    2353-9003
    Pojawia się w:
    International Journal of Applied Mechanics and Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    New iterative method of solving nonlinear equations in fluid mechanics
    Autorzy:
    Palivets, M.
    Andreev, E.
    Bakshtanin, A.
    Benin, D.
    Snezhko, V.
    Powiązania:
    https://bibliotekanauki.pl/articles/2106452.pdf
    Data publikacji:
    2021
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    trzęsienie ziemi
    mechanika płynów
    porowatość
    Adomian Decomposition Method ADM
    earthquake
    filtration
    fluid mechanics
    iterative method
    nonlinear fractional partial differential equations
    porous medium
    Opis:
    This paper presents the results of applying a new iterative method to linear and nonlinear fractional partial differential equations in fluid mechanics. A numerical analysis was performed to find an exact solution of the fractional wave equation and fractional Burgers’ equation, as well as an approximate solution of fractional KdV equation and fractional Boussinesq equation. Fractional derivatives of the order are described using Caputo's definition with 01<α≤ or 12<α≤. A comparative analysis of the results obtained using a new iterative method with those obtained by the Adomian decomposition method showed the first method to be more efficient and simple, providing accurate results in fewer computational operations. Given its flexibility and ability to solve nonlinear equations, the iterative method can be used to solve more complex linear and nonlinear fractional partial differential equations.
    Źródło:
    International Journal of Applied Mechanics and Engineering; 2021, 26, 3; 163--176
    1734-4492
    2353-9003
    Pojawia się w:
    International Journal of Applied Mechanics and Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Dedicated spectral method of Boolean function decomposition
    Autorzy:
    Porwik, P.
    Stanković, R. S.
    Powiązania:
    https://bibliotekanauki.pl/articles/908408.pdf
    Data publikacji:
    2006
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    funkcja boolowska
    dekompozycja rozłączna
    spektrum Walsha
    współczynnik autokorelacji
    Boolean function
    Walsh spectrum
    autocorrelation coefficients
    disjoint decomposition
    Opis:
    Spectral methods constitute a useful tool in the analysis and synthesis of Boolean functions, especially in cases when other methods reduce to brute-force search procedures. There is renewed interest in the application of spectral methods in this area, which extends also to the closely connected concept of the autocorrelation function, for which spectral methods provide fast calculation algorithms. This paper discusses the problem of spectral decomposition of Boolean functions using the Walsh transform and autocorrelation characteristics.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2006, 16, 2; 271-278
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An efficient algorithm for adaptive total variation based image decomposition and restoration
    Autorzy:
    Liu, X.
    Huang, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/330619.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    image decomposition
    image restoration
    adaptive total variation
    H-1 norm
    split Bregman method
    dekompozycja obrazu
    odtworzenie obrazu
    wariacja zupełna adaptacyjna
    metoda Bregmana
    Opis:
    With the aim to better preserve sharp edges and important structure features in the recovered image, this article researches an improved adaptive total variation regularization and H-1 norm fidelity based strategy for image decomposition and restoration. Computationally, for minimizing the proposed energy functional, we investigate an efficient numerical algorithm—the split Bregman method, and briefly prove its convergence. In addition, comparisons are also made with the classical OSV (Osher–Sole–Vese) model (Osher et al., 2003) and the TV-Gabor model (Aujol et al., 2006), in terms of the edge-preserving capability and the recovered results. Numerical experiments markedly demonstrate that our novel scheme yields significantly better outcomes in image decomposition and denoising than the existing models.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2014, 24, 2; 405-415
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Area-oriented technology mapping for LUT-based logic blocks
    Autorzy:
    Kubica, M.
    Kania, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/331370.pdf
    Data publikacji:
    2017
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    SMTBDD
    FPGA
    synthesis method
    decomposition technique
    metoda syntezy
    technika rozkładu
    Opis:
    One of the main aspects of logic synthesis dedicated to FPGA is the problem of technology mapping, which is directly associated with the logic decomposition technique. This paper focuses on using configurable properties of CLBs in the process of logic decomposition and technology mapping. A novel theory and a set of efficient techniques for logic decomposition based on a BDD are proposed. The paper shows that logic optimization can be efficiently carried out by using multiple decomposition. The essence of the proposed synthesis method is multiple cutting of a BDD. A new diagram form called an SMTBDD is proposed. Moreover, techniques that allow finding the best technology mapping oriented to configurability of CLBs are presented. In the experimental section, the presented method (MultiDec) is compared with academic and commercial tools. The experimental results show that the proposed technology mapping strategy leads to good results in terms of the number of CLBs.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2017, 27, 1; 207-222
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A fast neural network learning algorithm with approximate singular value decomposition
    Autorzy:
    Jankowski, Norbert
    Linowiecki, Rafał
    Powiązania:
    https://bibliotekanauki.pl/articles/330870.pdf
    Data publikacji:
    2019
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    Moore–Penrose pseudoinverse
    radial basis function network
    extreme learning machine
    kernel method
    machine learning
    singular value decomposition
    deep extreme learning
    principal component analysis
    pseudoodwrotność Moore–Penrose
    radialna funkcja bazowa
    maszyna uczenia ekstremalnego
    uczenie maszynowe
    analiza składników głównych
    Opis:
    The learning of neural networks is becoming more and more important. Researchers have constructed dozens of learning algorithms, but it is still necessary to develop faster, more flexible, or more accurate learning algorithms. With fast learning we can examine more learning scenarios for a given problem, especially in the case of meta-learning. In this article we focus on the construction of a much faster learning algorithm and its modifications, especially for nonlinear versions of neural networks. The main idea of this algorithm lies in the usage of fast approximation of the Moore–Penrose pseudo-inverse matrix. The complexity of the original singular value decomposition algorithm is O(mn2). We consider algorithms with a complexity of O(mnl), where l < n and l is often significantly smaller than n. Such learning algorithms can be applied to the learning of radial basis function networks, extreme learning machines or deep ELMs, principal component analysis or even missing data imputation.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2019, 29, 3; 581-594
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Stabilized model reduction for nonlinear dynamical systems through a contractivity-preserving framework
    Autorzy:
    Chaturantabut, Saifon
    Powiązania:
    https://bibliotekanauki.pl/articles/1838159.pdf
    Data publikacji:
    2020
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    model order reduction
    ordinary differential equation
    partial differential equation
    proper orthogonal decomposition
    discrete empirical interpolation method
    redukcja rzędu modelu
    równanie różniczkowe zwyczajne
    równanie różniczkowe cząstkowe
    rozkład ortogonalny
    Opis:
    This work develops a technique for constructing a reduced-order system that not only has low computational complexity, but also maintains the stability of the original nonlinear dynamical system. The proposed framework is designed to preserve the contractivity of the vector field in the original system, which can further guarantee stability preservation, as well as provide an error bound for the approximated equilibrium solution of the resulting reduced system. This technique employs a low-dimensional basis from proper orthogonal decomposition to optimally capture the dominant dynamics of the original system, and modifies the discrete empirical interpolation method by enforcing certain structure for the nonlinear approximation. The efficiency and accuracy of the proposed method are illustrated through numerical tests on a nonlinear reaction diffusion problem.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2020, 30, 4; 615-628
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-8 z 8

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