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EN
We discuss a nice composition properties related to algorithms for computation of N-roots. Our approach gives direct proof that a version of Newton's iterative algorithm is of order 2. A basic tool used in this note are properties of rational function Φ(w; z) = z-w/(z+w), which was used earlier in [1] in the case of algorithms for computations of square roots.
EN
We discuss a less known but surprising fact: a very old algorithm for computing square root known as the Bhaskara-Brouncker algorithm contains another and faster algorithms. A similar approach was obtained earlier by A.K. Yeyios [8] in 1992. By the way, we shall present a few useful facts as an essential completion of [8]. In particular, we present a direct proof that k – th Yeyios iterative algorithm is of order k. We also observe that Chebyshev polynomials Tn and Un are a special case of a more general construction. The most valuable idea followed this paper is contained in applications of a simple rational function Φ(w; z) = z-w/z+w.
EN
The purpose of this paper is to study a split generalized mixed equilibrium problem and a fixed point problem for nonspreading mappings in real Hilbert spaces. We introduce a new iterative algorithm and prove its strong convergence for approximating a common solution of a split generalized mixed equilibrium problem and a fixed point problem for nonspreading mappings in real Hilbert spaces. Our algorithm is developed by combining a modified accelerated Mann algorithm and a viscosity approximation method to obtain a new faster iterative algorithm for finding a common solution of these problems in real Hilbert spaces. Also, our algorithm does not require any prior knowledge of the bounded linear operator norm. We further give a numerical example to show the efficiency and consistency of our algorithm. Our result improves and compliments many recent results previously obtained in this direction in the literature.
EN
The presented systems with magnetically coupled windings are solved with the finite element method. If the issue of voltage supply is analyzed, a system of linear equations with a partially skew-symmetric sparse matrix is obtained. Iterative methods used to solve a system of equations are particularly effective for symmetric matrices. Resultant equations can be reduced to this symmetrical form by using the method known from the literature [1]. The ratio of the maximum to the minimum eigenvalue of the main matrix of this circuit, which is the condition number, is however very high. This means that the problem is ill-conditioned and leads to a very long iterative solution process. The method presented in the article allows for a direct solution of a system of equations on its part, corresponding to high eigenvalues of the system matrix. The remaining part of the system of equations is solved by iterative methods. This part has much better condition number, and therefore the computational process is fast. The proposed iterative process depends on multiplication of a sparse matrix by vectors. It is not necessary (and possible) to store the entire matrix. This is especially important for larger sizes of a matrix.
5
Content available Algorytmy równoległe w języku programowania C#
PL
W artykule opisano możliwość łatwego implementowania równoległych algorytmów w języku programowania C# . Zwrócono szczególną uwagę na zastosowanie metody For klasy Parallel dostępnej na platformie Microsoft.NET.
EN
The article describes the ability to easily implement parallel algorithms in the C# programming language. Special attention was paid to the application of the method For class Parallel available on the Microsoft .NET platform.
PL
Przedstawiono ideę iteracyjnej metody wariacyjnej VIM i pokazano jej skuteczność w analizie zwichrzenia pryzmatycznej belki poddanej obciążeniu równomiernie rozłożonemu. Wartości obciążeń krytycznych uzyskanych z rozwiązań analitycznych przy zastosowaniu metody VIM porównano z wartościami obliczonymi metodą elementów skończonych.
EN
The paper presents the idea of variational iteration method (VIM) and indicates its efficiency in stability analysis of prismatic beam under uniformly distributed load. The results obtained by using VIM were compared with the critical loads computed by finite element method.
PL
W artykule podano równoległą implementację metod rozwiązywania układu równań liniowych z macierzą rzadką w języku programowania UPC (Unified Parallel C). Uwzględniono możliwości środowiska programistycznego Berkeley UPC oraz format spakowanych wierszy CSR (Compressed Sparse Row).
EN
Paper described a parallel implementation of the iterative methods for solving linear equation systems with sparse matrix in the UPC programming language (Unified Parallel C). Possibilities of the Berkeley UPC development environment and the CSR packed rows format (Compressed Sparse Row) were included.
8
Content available remote Modeling of polymer/clay nanocomposites by an iterative micromechanical approach
EN
An iterative micromechanical method is presented in order to predict the elastic constants of composites and nanocomposites including arbitrarily oriented reinforcement particles. The proposed method is capable of introducing into the matrix any kind of heterogeneity based on its dimension, orientation, mechanical properties and volume fraction. The efficiency and convergence of solution method is studied by computing the elasticity tensor of a unidirectional particulate composite. It is then applied to model the elastic behavior of nylon-6/clay nanocomposite with taking into consideration the probability distribution of aspect ratio and orientation of effective particles. The results are validated by comparison with available experimental data.
9
Content available remote Computation of current harmonics from voltage waveforms: optimization approach
EN
The group harmonic compensation in electrical systems, especially compensation of scattered nonlinear loads, needs a proper approach to acquisition of reference signals controlling compensators. Such signal cannot be worked out from the current of individual load. The reference signal should be obtained from voltage waveform. Presented method of compensation current estimation can be classified as an invasive method. The change of voltage waveform caused by compensator current is the source of information for proposed iterative algorithm. This algorithm allows to compute the current reducing voltage distortion. It has been shown that optimization algorithms available in MATLAB can be used for considered purpose. Numerical tests have been made for the example nonlinear circuit. The quasi-Newton algorithm was used in these tests.
PL
Kompensacja równoległa harmonicznych dla grup odbiorników, szczególnie rozproszonych, stwarza specjalne wymagania w odniesieniu do sygnału sterującego kompensator. Problemem jest jaki prąd powinien generować taki kompensator. Prąd ten nie może być bezpośrednio uzyskany na podstawie prądów odbiorników, które mogą być nawet niedostępne dla pomiarów. Sygnał sterujący może być obliczany w oparciu o przebieg napięcia. Taka metoda jest prezentowana w pracy. Metoda ta może być sklasyfikowana jako inwazyjna i iteracyjna. Źródłem informacji jest zmiana przebiegu napięcia spowodowana zmianą przebiegu prądu kompensatora. Pokazano, że do tego celu może być użyty algorytm optymalizacyjny dostępny w programie MATLAB. Przedstawiono testy uzyskane na przykładzie kilku obwodów nieliniowych.
10
EN
A class of contact problems with friction in elastostatics is considered. Under a certain restriction on the friction coefficient, the convergence of the two-step iterative method proposed by P.D. Panagiotopoulos is proved. Its applicability is discussed and compared with two other iterative methods, and the computed results are presented.
EN
Interesting structural considerations can be derived from comparison of the topologies and forms of regulators obtained by the pole-placement design, the GTDOF and the MPC. Practical advice is given to the polynomial orders of the MPC. A new simple method is introduced for iterative ID and control based on these findings.
PL
W artykule przedstawiono przykłady praktycznych sposobów rozwiązywania zagadnień odwrotnych znajdujące zastosowanie do wyznaczania cieplnych charakterystyk materiałów. Podano założenia, sformułowania oraz przeprowadzono analizę iteracyjnych i bezpośrednich metod rozwiązywania tych zagadnień. Wskazano na potrzebę rozwoju tych metod w powiązaniu z metodyką pieczołowicie przeprowadzonego eksperymentu.
EN
In the paper the examples of practical solutions of inverse problem methods applied to thermal material data determination are presented. The assumptions and rules and also analyses of iterative and direct methods are shown. It is indicated that the development of those methods, connected with careful experiment methodology, are needed.
13
Content available remote Własności niezupełnego rozkładu LDLt w iteracyjnych rozwiązań równań MES
PL
W pracy przedstawiono niektóre aspekty stosowania metody gradientów sprzężonych do rozwiązywania dużych układów równań liniowych metodą elementów skończonych. Wykazano atrakcyjność stosowania schematów iteracyjnych w stosunku do metod bezpośrednich oraz przeanalizowano wpływ uporządkowania układu równań na szybkość zbieżności iteracji.
EN
The efficiency of the preconditioned conjugate gradient method applied to solving large sparse linear equation derived from finite element method has been studied.
14
Content available remote Design of foundation rafts by uncoupled iterative method
EN
The authors developed a calculation module into a commercial finite element analysis (FEA) program, which is capable of calculating foundation rafts quickly, with correct results for the engineering practice. The calculation method is based on the so-called 'uncoupled iterative method', wherein the structure and the soil continuum are analysed separately. The results of one analysis form the boundary conditions for the subsequent analysis as part of an iterative process.The connection between the raft and the soil is considered to be represented by the bedding modulus of the raft and by the soil stresses. The method provides the same displacements for the raft as for the soil surface, provided sufficient convergence can be reached if the raft is not elevated from the soil.
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