摘要 :
In this paper, we present a new modified Newton method for solving a non linear algebraic equation by using the well-known Nedzhibov's method [D. K. R. Babajee, M. Z. Dauhoo, An analysis of the properties of the variants of Newton...
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In this paper, we present a new modified Newton method for solving a non linear algebraic equation by using the well-known Nedzhibov's method [D. K. R. Babajee, M. Z. Dauhoo, An analysis of the properties of the variants of Newton's method with third order convergence, Applied Mathematics and Computation 183 (1) (2006), 659-684]. We proposed a new iteration method and we show by one equation that this new iteration method is more quickly convergence than Newton's method. (C) 2007 Elsevier Inc. All rights reserved.
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Purpose - The purpose of this paper is to apply, for the first time, the authors' newly developed perturbation iteration method to heat transfer problems. The effectiveness of the new method in nonlinear heat transfer problems wil...
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Purpose - The purpose of this paper is to apply, for the first time, the authors' newly developed perturbation iteration method to heat transfer problems. The effectiveness of the new method in nonlinear heat transfer problems will be tested. Design/methodology/approach - Nonlinear heat transfer problems are solved by perturbation iteration method. They are also solved by the well-known technique variational iteration method in the literature. Findings - It is found that perturbation iteration solutions converge faster to the numerical solutions. More accurate results can be achieved with this new method for nonlinear heat transfer problems. Research limitations/implications - A few iterations are actually sufficient. Further iterations need symbolic packages to calculate the solutions. Practical implications - This new technique can practically be applied to many heat and flow problems. Originality/value - The new perturbation iteration technique is successfully implemented to nonlinear heat transfer problems. Results show good agreement with the direct numerical simulations and the method performs better than the existing variational iteration method.
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In this paper, Newton's iterative method to solve the nonlinear matrix equation x + A* X-n A = Q is studied. For the given initial matrix Q, the main results that the matrix sequence generated by the iterative method is contained ...
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In this paper, Newton's iterative method to solve the nonlinear matrix equation x + A* X-n A = Q is studied. For the given initial matrix Q, the main results that the matrix sequence generated by the iterative method is contained in a fixed open ball, and that the matrix sequence generated by the iterative method converges to the only solution of the nonlinear matrix equation in a fixed closed ball are proved. In addition, the error estimate of the approximate solution in the closed ball and a numerical example to illustrate the convergence results are given.
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In this paper we study inexact inverse iteration for solving the generalised eigenvalue problem Ax = λMx. We show that inexact inverse iteration is a modified Newton method and hence obtain convergence rates for various versions ...
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In this paper we study inexact inverse iteration for solving the generalised eigenvalue problem Ax = λMx. We show that inexact inverse iteration is a modified Newton method and hence obtain convergence rates for various versions of inexact inverse iteration for the calculation of an algebraically simple eigenvalue. In particular, if the inexact solves are carried out with a tolerance chosen proportional to the eigenvalue residual then quadratic convergence is achieved. We also show how modifying the right hand side in inverse iteration still provides a convergent method, but the rate of convergence will be quadratic only under certain conditions on the right hand side. We discuss the implications of this for the preconditioned iterative solution of the linear systems. Finally we introduce a new ILU preconditioner which is a simple modification to the usual preconditioner, but which has advantages both for the standard form of inverse iteration and for the version with a modified right hand side. Numerical examples are given to illustrate the theoretical results.
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Kotakemori et al. [H. Kotakemori, K. Harada, M. Morimoto, H. Niki. A comparison theorem for the iterative method with the preconditioner (I + S-max), Journal of Computational and Applied Mathematics 145 (2002) 373-378] have report...
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Kotakemori et al. [H. Kotakemori, K. Harada, M. Morimoto, H. Niki. A comparison theorem for the iterative method with the preconditioner (I + S-max), Journal of Computational and Applied Mathematics 145 (2002) 373-378] have reported that the convergence rate of the iterative method with a preconditioner P-m = (I + S) Was Superior to one of the modified Gauss-Seidel method under the condition. These authors derived a theorem comparing the Gauss-Seidel method with the proposed method. However, through application of a counter example, Wen Li [Wen Li, A note on the preconditioned GaussSeidel (GS) method for linear systems, journal of Computational and Applied Mathematics 182 (2005) 81-91] pointed Out that there exists a special matrix that does not satisfy this comparison theorem. In this note, we analyze the reason why such a to Counter example may be produced, and propose a preconditioner to overcome this problem. (C) 2009 Published by Elsevier B.V.
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A new hybrid iteration method (the hybrid's name was used by Luo [Xing-Guo Luo, Applied Mathematics and Computation 171 (2) (2005) 1171-11831) has been proposed for solving a non linear algebraic equation fix) = 0, by using Taylor...
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A new hybrid iteration method (the hybrid's name was used by Luo [Xing-Guo Luo, Applied Mathematics and Computation 171 (2) (2005) 1171-11831) has been proposed for solving a non linear algebraic equation fix) = 0, by using Taylor's theorem. In this paper, we proposed a new hybrid iteration method and we show by one equation that this new hybrid iteration method is more quickly convergent than Newton's method and hence than hybrid iteration method. (c) 2007 Elsevier Inc. All rights reserved.
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Efficient algorithms are described for computing the probability of detection for a binary integration when the probability of a threshold crossing changes from sample to sample. A binary integrator is exceeded (a hit occurs) in a...
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Efficient algorithms are described for computing the probability of detection for a binary integration when the probability of a threshold crossing changes from sample to sample. A binary integrator is exceeded (a hit occurs) in a sequence of N trials and declares a detection if the number of hits is at least as large as some number M, where O>or=M>or=N. J.S. Brunner (1990) described an efficient iterative method for the computation of these probabilities. The author gives an improved version of Brunner's algorithm, shows how to compute the probability of detection directly, and how to avoid needless computation when the probability of detection needs to be determined for one M only.
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This paper is concerned with a generalization of the Hermitian and skew-Hermitian splitting (HSS) iteration method for solving large sparse continuous Sylvester equations. The analysis shows that the GHSS iteration method will con...
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This paper is concerned with a generalization of the Hermitian and skew-Hermitian splitting (HSS) iteration method for solving large sparse continuous Sylvester equations. The analysis shows that the GHSS iteration method will converge under certain assumptions. Numerical results show that this new method is more efficient and robust than the existing ones. (C) 2015 Elsevier Inc. All rights reserved.
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In this paper we investigate and compare the variational iteration method and the successive approximations method for solving a class of nonlinear differential equations. We prove that these two methods are equivalent for solving...
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In this paper we investigate and compare the variational iteration method and the successive approximations method for solving a class of nonlinear differential equations. We prove that these two methods are equivalent for solving these types of equations.
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Electrical capacitance tomography (ECT) is a so-called 'soft-field' tomography technique. The linear back-projection (LBP) method is used widely for image reconstruction in ECT systems. It is numerically simple and computationally...
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Electrical capacitance tomography (ECT) is a so-called 'soft-field' tomography technique. The linear back-projection (LBP) method is used widely for image reconstruction in ECT systems. It is numerically simple and computationally fast because itinvolves only a single matrix-vector multiplication. However, the images produced by the LBP algorithm are generally qualitative rather than quantitative. This paper presents an image-reconstruction algorithm based on a modified Landweber iteration method that can greatly enhance the quality of the image when two distinct phases are present. In this algorithm a simple constraint is used as a regularization for computing a stabilized solution, with a better immunity to noise and faster convergence.Experimental results are presented
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