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21.
By further generalizing the skew-symmetric triangular splitting iteration method studied by Krukier, Chikina and Belokon (Applied Numerical Mathematics, 41 (2002), pp. 89–105), in this paper, we present a new iteration scheme, called the modified skew-Hermitian triangular splitting iteration method, for solving the strongly non-Hermitian systems of linear equations with positive definite coefficient matrices. We discuss the convergence property and the optimal parameters of this new method in depth. Moreover, when it is applied to precondition the Krylov subspace methods like GMRES, the preconditioning property of the modified skew-Hermitian triangular splitting iteration is analyzed in detail. Numerical results show that, as both solver and preconditioner, the modified skew-Hermitian triangular splitting iteration method is very effective for solving large sparse positive definite systems of linear equations of strong skew-Hermitian parts. 相似文献
22.
Teresa Regińska 《BIT Numerical Mathematics》2004,44(1):119-133
The paper concerns conditioning aspects of finite-dimensional problems arising when the Tikhonov regularization is applied
to discrete ill-posed problems. A relation between the regularization parameter and the sensitivity of the regularized solution
is investigated. The main conclusion is that the condition number can be decreased only to the square root of that for the
nonregularized problem. The convergence of solutions of regularized discrete problems to the exact generalized solution is
analyzed just in the case when the regularization corresponds to the minimal condition number. The convergence theorem is
proved under the assumption of the suitable relation between the discretization level and the data error. As an example the
method of truncated singular value decomposition with regularization is considered.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
23.
The semi‐iterative method (SIM) is applied to the hyper‐power (HP) iteration, and necessary and sufficient conditions are given for the convergence of the semi‐iterative–hyper‐power (SIM–HP) iteration. The root convergence rate is computed for both the HP and SIM–HP methods, and the quotient convergence rate is given for the HP iteration. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
24.
TANG Chen ZHANG Fang YAN Hai-Qing CHEN Zhan-Qing LUO Tao 《理论物理通讯》2005,44(3):435-439
We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the three- step explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponential fitting scheme to correct this prediction. This combination is called the three-step predictor-corrector of exponential fitting method. The three-step predictor-corrector of exponential fitting method is applied to numerically compute the coupled nonlinear Schroedinger equation and the nonlinear Schroedinger equation with varying coefficients. The numerical results show that the scheme is highly accurate. 相似文献
25.
We consider the problem of minimizing an SC1 function subject to inequality constraints. We propose a local algorithm whose distinguishing features are that: (a) a fast convergence rate is achieved under reasonable assumptions that do not include strict complementarity at the solution; (b) the solution of only linear systems is required at each iteration; (c) all the points generated are feasible. After analyzing a basic Newton algorithm, we propose some variants aimed at reducing the computational costs and, in particular, we consider a quasi-Newton version of the algorithm. 相似文献
26.
A new prediction technique is proposed for chaotic time series. The usefulness of the technique is thatit can kick off some false neighbor points which are not suitable for the local estimation of the dynamics systems. Atime-delayed embedding is used to reconstruct the underlying attractor, and the prediction model is based on the timeevolution of the topological neighboring in the phase space. We use a feedforward neural network to approximate thelocal dominant Lyapunov exponent, and choose the spatial neighbors by the Lyapunov exponent. The model is testedfor the Mackey-Glass equation and the convection amplitude of lorenz systems. The results indicate that this predictiontechnique can improve the prediction of chaotic time series. 相似文献
27.
一类非线性微分方程的脉冲镇定 总被引:5,自引:0,他引:5
针对一般形式的常微分系统提出了脉冲指数镇定的概念,具体研究了一类分离变量型非线性常微分方程的脉冲镇定问题,得到了该方程可脉冲指数镇定的充分判据,全文的概念及结论突出了脉冲在方程稳定性方面的控制效果。 相似文献
28.
Sh. M. Aitaliev 《International Applied Mechanics》2004,40(10):1065-1091
Some results on underground structures obtained by Kazakh mechanicians are reviewed. The review covers a period of the last forty years. Also results on the mechanics of special objects are discussed.Translated from Prikladnaya Mekhanika, Vol. 40, No. 10, pp. 3–36, October 2004. 相似文献
29.
30.
YaoKui ChenZhixiang 《分析论及其应用》2003,19(2):115-120
This paper gives the weighted Lp convergence rate estimations of the Gruenwald interpolatory polynomials based on the zeros of Chebyshev polymomials of the first kind,and proves that the order of the estimations is optimal for p≥1. 相似文献