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    Wyświetlanie 1-15 z 15
    Tytuł:
    Preconditioned Conjugate Gradient Method for Solution of Large Finite Element Problems on CPU and GPU
    Autorzy:
    Fialko, S. Y.
    Zeglen, F.
    Powiązania:
    https://bibliotekanauki.pl/articles/307602.pdf
    Data publikacji:
    2016
    Wydawca:
    Instytut Łączności - Państwowy Instytut Badawczy
    Tematy:
    conjugate gradient
    incomplete Cholesky factorization
    iterative solvers
    NVIDIA CUDA
    preconditioned conjugate gradient
    Opis:
    In this article the preconditioned conjugate gradient (PCG) method, realized on GPU and intended to solution of large finite element problems of structural mechanics, is considered. The mathematical formulation of problem results in solution of linear equation sets with sparse symmetrical positive definite matrices. The authors use incomplete Cholesky factorization by value approach, based on technique of sparse matrices, for creation of efficient preconditioning, which ensures a stable convergence for weakly conditioned problems mentioned above. The research focuses on realization of PCG solver on GPU with using of CUBLAS and CUSPARSE libraries. Taking into account a restricted amount of GPU core memory, the efficiency and reliability of GPU PCG solver are checked and these factors are compared with data obtained with using of CPU version of this solver, working on large amount of RAM. The real-life large problems, taken from SCAD Soft collection, are considered for such a comparison.
    Źródło:
    Journal of Telecommunications and Information Technology; 2016, 2; 26-33
    1509-4553
    1899-8852
    Pojawia się w:
    Journal of Telecommunications and Information Technology
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Iteratively reweighted least squares classifier and its l2- and l1-regularized Kernel versions
    Autorzy:
    Łęski, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/199904.pdf
    Data publikacji:
    2010
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    classifier design
    IRLS
    conjugate gradient optimization
    gradient projection
    Kernel matrix
    Opis:
    This paper introduces a new classifier design method based on regularized iteratively reweighted least squares criterion function. The proposed method uses various approximations of misclassification error, including: linear, sigmoidal, Huber and logarithmic. Using the represented theorem a kernel version of classifier design method is introduced. The conjugate gradient algorithm is used to minimize the proposed criterion function. Furthermore, .1-regularized kernel version of the classifier is introduced. In this case, the gradient projection is used to optimize the criterion function. Finally, an extensive experimental analysis on 14 benchmark datasets is given to demonstrate the validity of the introduced methods.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2010, 58, 1; 171-182
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Generalized ordered linear regression with regularization
    Autorzy:
    Łęski, J.
    Henzel, N.
    Powiązania:
    https://bibliotekanauki.pl/articles/201591.pdf
    Data publikacji:
    2012
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    linear regression
    IRLS
    OWA
    conjugate gradient optimization
    robust methods
    Opis:
    Linear regression analysis has become a fundamental tool in experimental sciences. We propose a new method for parameter estimation in linear models. The 'Generalized Ordered Linear Regression with Regularization' (GOLRR) uses various loss functions (including the o-insensitive ones), ordered weighted averaging of the residuals, and regularization. The algorithm consists in solving a sequence of weighted quadratic minimization problems where the weights used for the next iteration depend not only on the values but also on the order of the model residuals obtained for the current iteration. Such regression problem may be transformed into the iterative reweighted least squares scenario. The conjugate gradient algorithm is used to minimize the proposed criterion function. Finally, numerical examples are given to demonstrate the validity of the method proposed.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2012, 60, 3; 481-489
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Efficient Iterative Detection Based on Conjugate Gradient and Successive Over-Relaxation Methods for Uplink Massive MIMO Systems
    Autorzy:
    Labed, Smail
    Aounallah, Naceur
    Powiązania:
    https://bibliotekanauki.pl/articles/24200730.pdf
    Data publikacji:
    2023
    Wydawca:
    Instytut Łączności - Państwowy Instytut Badawczy
    Tematy:
    computational complexity
    conjugate gradient
    massive MIMO
    relaxation parameter
    signal detection
    Opis:
    Being a crucial aspect of fifth-generation (5G) mobile communications systems, massively multiple-input multipleoutput (mMIMO) architectures are expected to help achieve the highest key performance indicators. However, the huge numbers of antennas used in such systems make it difficult to determine the inversion of the signal channel matrix relied upon by several detection methods, hence posing a problem with accurate estimation of the symbols sent. In this paper, conjugate gradient (CG) and successive over-relaxation (SOR) methods are selected to construct a new iterative approach that avoids the matrix inversion computation issue. This suggested approach for uplink mMIMO detection is based on a joint cascade structure of both iterative methods. The CG method is first applied and adjusted for the initial solution, followed by the SOR method in the final iterations for terminal computations, resulting in an algorithm with robust performance and low computational complexity. Furthermore, the new hybrid scheme operates based on the relaxation parameter, whose value has a great impact on error performance and, whose optimal determination is necessary. Numerical simulations reveal that the proposed scheme is capable of significantly improving signal detection accuracy with minimum complexity. The simulation results indicated that the proposed detector outperforms CG and SOR detectors, achieves close to optimal performance, requires fewer iterations, and reduces complexity.
    Źródło:
    Journal of Telecommunications and Information Technology; 2023, 2; 1--9
    1509-4553
    1899-8852
    Pojawia się w:
    Journal of Telecommunications and Information Technology
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Operator-splitting and Lagrange multiplier domain decomposition methods for numerical simulation of two coupled Navier-Stokes fluids
    Autorzy:
    Bresch, D.
    Koko, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/908383.pdf
    Data publikacji:
    2006
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    dwoistość
    gradient sprzężony
    przepływ Naviera-Stokesa
    domain decomposition
    duality
    conjugate gradient
    Navier-Stokes flows
    Opis:
    We present a numerical simulation of two coupled Navier-Stokes flows, using operator-splitting and optimization-based nonoverlapping domain decomposition methods. The model problem consists of two Navier-Stokes fluids coupled, through a common interface, by a nonlinear transmission condition. Numerical experiments are carried out with two coupled fluids; one with an initial linear profile and the other in rest. As expected, the transmission condition generates a recirculation within the fluid in rest.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2006, 16, 4; 419-429
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A conjugate gradient method with quasi-Newton approximation
    Autorzy:
    Koko, Jonas
    Powiązania:
    https://bibliotekanauki.pl/articles/1208176.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Newton and quasi-Newton methods
    unconstrained high-dimensional optimization
    conjugate gradient methods
    Opis:
    The conjugate gradient method of Liu and Storey is an efficient minimization algorithm which uses second derivatives information, without saving matrices, by finite difference approximation. It is shown that the finite difference scheme can be removed by using a quasi-Newton approximation for computing a search direction, without loss of convergence. A conjugate gradient method based on BFGS approximation is proposed and compared with existing methods of the same class.
    Źródło:
    Applicationes Mathematicae; 2000, 27, 2; 153-165
    1233-7234
    Pojawia się w:
    Applicationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Application of high-performance techniques for solving linear systems of algebraic equations
    Autorzy:
    Grzonka, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/307729.pdf
    Data publikacji:
    2013
    Wydawca:
    Instytut Łączności - Państwowy Instytut Badawczy
    Tematy:
    Advanced Vector Extension
    conjugate gradient method
    incomplete Cholesky factorization
    preconditioning
    vector registers
    Opis:
    Solving many problems in mechanics, engineering, medicine and other (e.g., diffusion tensor magnetic resonance imaging or finite element modeling) requires the efficient solving of algebraic equations. In many cases, such systems are very complex with a large number of linear equations, which are symmetric positive-defined (SPD). This paper is focused on improving the computational efficiency of the solvers dedicated for the linear systems based on incomplete and noisy SPD matrices by using preconditioning technique – Incomplete Cholesky Factorization, and modern set of processor instructions – Advanced Vector Extension. Application of these techniques allows to fairly reduce the computational time, number of iterations of conventional algorithms and improve the speed of calculation.
    Źródło:
    Journal of Telecommunications and Information Technology; 2013, 4; 85-91
    1509-4553
    1899-8852
    Pojawia się w:
    Journal of Telecommunications and Information Technology
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Computational and Statistical Aspects of Determining Ships Position
    Autorzy:
    Drapella, A.
    Morgaś, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/320950.pdf
    Data publikacji:
    2017
    Wydawca:
    Polskie Forum Nawigacyjne
    Tematy:
    determining ship’s position
    Least Square method
    conjugate gradient
    Monte Carlo method
    Opis:
    In its mathematical essence, the task of determining ship’s position coordinates, is to minimize appropriately defined goal function. This paper proposes to use the method of conjugate gradient for this purpose. The reason is that calculations may be performed in some seconds time because Microsoft and Apache implemented the conjugate gradient method as a tool called the Solver and embedded this tool in their widely offered and popular spreadsheets, namely Excel and the Open Office Calc, respectively. Further in this paper it is shown how to precisely assess errors of ship’s position coordinates with the Monte Carlo method that employs the Solver.
    Matematyczna istota wyznaczania współrzędnych pozycji okrętu to minimalizacja odpowiednio zdefiniowanej funkcji celu. Artykuł proponuje wykorzystanie do tego metody gradientu sprzężonego. Dzięki niej obliczenia mogą być wykonane w kilka sekund, ponieważ Microsoft i Apache zaimplementowały metodę gradientu sprzężonego jako narzędzie nazwane Solver i umieściły je w swych szeroko oferowanych i popularnych arkuszach kalkulacyjnych: Excelu i Open Office Calc. W artykule pokazano także, jak precyzyjnie określić błędy oszacowania współrzędnych pozycji okrętu metodą Monte Carlo.
    Źródło:
    Annual of Navigation; 2017, 24; 5-18
    1640-8632
    Pojawia się w:
    Annual of Navigation
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A parallel algorithm of icsym forcomplexsymmetric linear systems in quantum chemistry
    Autorzy:
    Zhang, Y.
    Lv, Q.
    Xiao, M.
    Xie, G.
    Breitkopf, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/305677.pdf
    Data publikacji:
    2018
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    complex symmetric linear systems
    parallel computing
    improved conjugate gradient-type iterative algorithm (ICSYM)
    Opis:
    Computational effort is a common issue for solving large-scale complex symmetric linear systems, particularly in quantum chemistry applications. In order to alleviate this problem, we propose a parallel algorithm of improved conjugate gradient-type iterative (ICSYM). Using three-term recurrence relation and or- thogonal properties of residual vectors to replace the tridiagonalization process of classical CSYM, which allows to decrease the degree of the reduce-operator from two to one communication at each iteration and to reduce the amount of vector updates and vector multiplications. Several numerical examples are implemented to show that high performance of proposed improved version is obtained both in convergent rate and in parallel efficiency.
    Źródło:
    Computer Science; 2018, 19 (4); 385-401
    1508-2806
    2300-7036
    Pojawia się w:
    Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    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:
    On the Choice of Subspace for Iterative Methods for Linear Discrete Ill-Posed Problems
    Autorzy:
    Calvetti, D.
    Lewis, B.
    Reichel, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/908057.pdf
    Data publikacji:
    2001
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    metoda sprzężonych gradientów
    problem niewłaściwie postawiony
    minimal residual method
    conjugate gradient method
    ill-posed problems
    Opis:
    Many iterative methods for the solution of linear discrete ill-posed problems with a large matrix require the computed approximate solutions to be orthogonal to the null space of the matrix. We show that when the desired solution is not smooth, it may be possible to determine meaningful approximate solutions with less computational work by not imposing this orthogonality condition.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2001, 11, 5; 1069-1092
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Comparative study of conjugate gradient algorithms performance on the example of steady-state axisymmetric heat transfer problem
    Autorzy:
    Ocłoń, P.
    Łopata, S.
    Nowak, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/240612.pdf
    Data publikacji:
    2013
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    conjugate gradient method
    finite element method
    finned circular tube
    metoda gradientu sprzężonego
    metoda elementów skończonych
    rury żebrowane
    Opis:
    The finite element method (FEM) is one of the most frequently used numerical methods for finding the approximate discrete point solution of partial differential equations (PDE). In this method, linear or nonlinear systems of equations, comprised after numerical discretization, are solved to obtain the numerical solution of PDE. The conjugate gradient algorithms are efficient iterative solvers for the large sparse linear systems. In this paper the performance of different conjugate gradient algorithms: conjugate gradient algorithm (CG), biconjugate gradient algorithm (BICG), biconjugate gradient stabilized algorithm (BICGSTAB), conjugate gradient squared algorithm (CGS) and biconjugate gradient stabilized algorithm with l GMRES restarts (BICGSTAB(l)) is compared when solving the steady-state axisymmetric heat conduction problem. Different values of l parameter are studied. The engineering problem for which this comparison is made is the two-dimensional, axisymmetric heat conduction in a finned circular tube.
    Źródło:
    Archives of Thermodynamics; 2013, 34, 3; 15-44
    1231-0956
    2083-6023
    Pojawia się w:
    Archives of Thermodynamics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Symmetrized semi-smooth Newton method for solving 3D contact problems
    Symetrizovaná nehladká Newtonova metoda pro rešení 3D kontaktních úloh
    Autorzy:
    Kucera, R.
    Haslinger, J.
    Motycková, K.
    Markopoulos, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/112650.pdf
    Data publikacji:
    2017
    Wydawca:
    STE GROUP
    Tematy:
    contact problem
    Tresca friction
    semi-smooth Newton methods
    conjugate gradient method
    gradient projection
    convergence rate
    zagadnienie kontaktowe
    tarcie Treski
    metoda gradientu sprzężonego
    rzutowanie gradientu
    szybkość konwergencji
    Opis:
    The semi-smooth Newton method for solving discretized contact problems with Tresca friction in three space dimensions is analyzed. The slanting function is approximated to get symmetric inner linear systems. The primal-dual algorithm is transformed into the dual one so that the conjugate gradient method can be used. The R-linear convergence rate is proved for an inexact globally convergent variant of the method. Numerical experiments conclude the paper. The contact problems are important in many practical applications, e.g., biological processes, design of machines, transportation systems, metal forming, or medicine (bone replacements).
    V práci je analyzována nehladká Newtonova metoda pro rešení diskretizovaných kontaktních úloh s Trescovým trením ve trech prostorových dimenzích. Slanting funkce je aproximována za úcelem získání symetrických vnitrních lineárních úloh. Pro použití metody sdružených gradientu je primárne-duální algoritmus preveden na duální. R-lineární rychlost konvergence je dokázána pro nepresnou globálne konvergentní variantu metody. Záverem jsou uvedeny numerické experimenty. Kontaktní úlohy mají radu významných aplikací, napr. biologické procesy, design stroju a prepravních systému, tvárení kovu nebo medicína (modelování kostních náhrad).
    Źródło:
    Systemy Wspomagania w Inżynierii Produkcji; 2017, 6, 4; 286-293
    2391-9361
    Pojawia się w:
    Systemy Wspomagania w Inżynierii Produkcji
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Two implementations of the preconditioned conjugate gradient method on heterogeneous computing grids
    Autorzy:
    Collignon, T. P.
    Van Gijzen, M. B.
    Powiązania:
    https://bibliotekanauki.pl/articles/907778.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    przetwarzanie siatkowe
    system liniowy
    metoda iteracyjna
    gradient sprzężony
    przepływ pęcherzykowy
    grid computing
    large sparse linear systems
    iterative methods
    conjugate gradient method
    Chronopoulos/Gear CG
    GridSolve middleware
    bubbly flows
    Opis:
    Efficient iterative solution of large linear systems on grid computers is a complex problem. The induced heterogeneity and volatile nature of the aggregated computational resources present numerous algorithmic challenges. This paper describes a case study regarding iterative solution of large sparse linear systems on grid computers within the software constraints of the grid middleware GridSolve and within the algorithmic constraints of preconditioned Conjugate Gradient (CG) type methods. We identify the various bottlenecks induced by the middleware and the iterative algorithm. We consider the standard CG algorithm of Hestenes and Stiefel, and as an alternative the Chronopoulos/Gear variant, a formulation that is potentially better suited for grid computing since it requires only one synchronisation point per iteration, instead of two for standard CG. In addition, we improve the computation-to-communication ratio by maximising the work in the preconditioner. In addition to these algorithmic improvements, we also try to minimise the communication overhead within the communication model currently used by the GridSolve middleware. We present numerical experiments on 3D bubbly flow problems using heterogeneous computing hardware that show lower computing times and better speed-up for the Chronopoulos/Gear variant of conjugate gradients. Finally, we suggest extensions to both the iterative algorithm and the middleware for improving granularity.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2010, 20, 1; 109-121
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Quartic non-polynomial spline solution for solving two-point boundary value problems by using Conjugate Gradient iterative method
    Autorzy:
    Justine, H.
    Chew, J. V. L.
    Sulaiman, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/122546.pdf
    Data publikacji:
    2017
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    two-point boundary value problems
    quartic non-polynomial spline
    Conjugate Gradient
    Successive Over-Relaxation
    Gauss-Seidel
    dwupunktowe problemy brzegowe
    metoda gradientu sprzężonego
    metoda Gaussa-Seidela
    metoda iteracyjna
    Opis:
    Solving two-point boundary value problems has become a scope of interest among many researchers due to its significant contributions in the field of science, engineering, and economics which is evidently apparent in many previous literary publications. This present paper aims to discretize the two-point boundary value problems by using a quartic non-polynomial spline before finally solving them iteratively with Conjugate Gradient (CG) method. Then, the performances of the proposed approach in terms of iteration number, execution time and maximum absolute error are compared with Gauss-Seidel (GS) and Successive Over-Relaxation (SOR) iterative methods. Based on the performances analysis, the two-point boundary value problems are found to have the most favorable results when solved using CG compared to GS and SOR methods.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2017, 16, 1; 41-50
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-15 z 15

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