105,331 research outputs found

    Rank-1 Tensor Approximation Methods and Application to Deflation

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    Because of the attractiveness of the canonical polyadic (CP) tensor decomposition in various applications, several algorithms have been designed to compute it, but efficient ones are still lacking. Iterative deflation algorithms based on successive rank-1 approximations can be used to perform this task, since the latter are rather easy to compute. We first present an algebraic rank-1 approximation method that performs better than the standard higher-order singular value decomposition (HOSVD) for three-way tensors. Second, we propose a new iterative rank-1 approximation algorithm that improves any other rank-1 approximation method. Third, we describe a probabilistic framework allowing to study the convergence of deflation CP decomposition (DCPD) algorithms based on successive rank-1 approximations. A set of computer experiments then validates theoretical results and demonstrates the efficiency of DCPD algorithms compared to other ones

    A Nonlinear Approximate Solution to the Damped Pendulum Derived Using the Method of Successive Approximations

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    An approximate analytic solution to the damped pendulum is derived using the method of successive approximations to obtain a nonlinear approximation for the system. We take the approximate solution to the undamped pendulum using the method of successive approximations and compare it to the damped pendulum solution when a linear approximation is used. By looking at these two solutions, we can make an educated guess about the form of the general, approximate solution to the nonlinear damped pendulum. By adjusting the initial guesses and the initial conditions, we derive approximate solutions in three ways. Using MATLAB, the approximate solutions are compared to the full numerical solution through the Euler-Cromer method. To determine how accurate the approximations are, the errors of the approximations are calculated relative to the full numerical Euler-Cromer solution. Each new approximation came with a significant decrease in error, with the final error being 0.0099. This resulted in an improvement to the method of successive approximations. Finally, our best approximation is compared to an available and previously published work

    Order reductions of Lorentz-Dirac-like equations

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    We discuss the phenomenon of preacceleration in the light of a method of successive approximations used to construct the physical order reduction of a large class of singular equations. A simple but illustrative physical example is analyzed to get more insight into the convergence properties of the method.Comment: 6 pages, LaTeX, IOP macros, no figure

    An Accelerate Process for the Successive Approximations Method In the Case of Monotonous Convergence

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    We study an iterative process to accelerate the successive approximations method in a monotonous convergence framework. It consists in interrupting the sequence of the successive approximations method produced at the kth iteration and substituting it by a combination of the element of the sequence produced at the iterate k + 1 and an extrapolation vector. The latter uses a parameter which can be calculated mathematically. We illustrate numerically this process by studying a freeboundary problems class

    Maximal Acceleration Effects in Kerr Space

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    We consider a model in which accelerated particles experience line--elements with maximal acceleration corrections that are introduced by means of successive approximations. It is shown that approximations higher than the first need not be considered. The method is then applied to the Kerr metric. The effective field experienced by accelerated test particles contains corrections that vanish in the limit 0\hbar\to 0, but otherwise affect the behaviour of matter greatly. The corrections generate potential barriers that are external to the horizon and are impervious to classical particles.Comment: 16 pages, 10 figures, to appear on Phys. Lett.

    Solution of Volterra integral equations by method of successive approximations

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    Bu çalışmada farklı tipte integral denklemler ve onların çözümleriyle ilgili durumlar incelenmiştir. Bu denklemler yaklaşık ardışıklar yöntemiyle çözülmüştür. Bu çalışma dört bölümden oluşur. Birinci bölümde, önceki dönemlerde yapılan çalışmalar ve bu tezde yapılacak olanlar anlatılmıştır. İkinci bölümde ise, gerekli temel tanımlar, Volterra ve Fredholm integral denklemlerin yaklaşık ardışıklar yöntemiyle çözümü üzerinde durulmuştur. Üçüncü bölümde ise, R1, R2, R3 `deki sabit katsayılı dalga denklemlerinin D'alambert, Poisson ve Kirchgoff integral denklemlerine indirgenebileceğine ve bunların çözümleri üzerinde durulmuş, varlık ve teklik teoremleri ispatlanmıştır. Dördüncü bölümde ise fonksiyon katsayılı dalga denklemleri ve bunların çözümleri üzerinde durulmuştur. Beşinci bölümde elde edilen sonuçlar verildi.Different type of integral equations and their solutions are considered in this thesis. These integral equations were solved by the successive approximations. This thesis consists of four chapters. In the first chapter, history of integral equations are given and which were studied. In the second chapter, the basic concepts are given which are necessary for the subject Volterra and Fredholm integral equations were solved by the successive approximations method. In the third chapter, initial value problems for hyperbolic equations with constant confficients in R1, R2, R3 are reducible to D'alambert, Poisson and Krichhoff's integral equations were solved by the successive approximations. The existence and uniqueness theorems for the solution of an integral equations. In the fourth chapter wave equation with the funcion velocity are studied. The existence and uniquenses theorems for the solution of an integral equations. The fifth chapter involves the conclusion of study
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