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121.
This work is a survey of results for ill-posed Cauchy problems for PDEs of the author with co-authors starting from 1991. A universal method of the regularization of these problems is presented here. Even though the idea of this method was previously discussed for specific problems, a universal approach of this paper was not discussed, at least in detail. This approach consists in constructing of such Tikhonov functionals which are generated by unbounded linear operators of those PDEs. The approach is quite general one, since it is applicable to all PDE operators for which Carleman estimates are valid. Three main types of operators of the second order are among them: elliptic, parabolic and hyperbolic ones. The key idea is that convergence rates of minimizers are established using Carleman estimates. Generalizations to nonlinear inverse problems, such as problems of reconstructions of obstacles and coefficient inverse problems are also feasible. 相似文献
122.
123.
124.
Wei LiuQimin Zhang 《Applied mathematics and computation》2011,218(8):3973-3980
In general, most of stochastic age-structured system of three species do not have explicit solutions, thus numerical approximation schemes are invaluable tools for exploring their properties. The aim of this paper is to investigate the convergence of numerical approximation solution to the true solution for stochastic age-structured system of three species. 相似文献
125.
126.
We propose least squares estimators of E(Y/X=x) for Y censored on the right by R and min(Y,R) left censored. We establish their convergence in the L2-norm. This work extends a known result in the context of right censoring. 相似文献
127.
Sergey G. Foss Anatolii A. Puhalskii 《Stochastic Processes and their Applications》2011,121(2):288-313
We consider a random walk with a negative drift and with a jump distribution which under Cramér’s change of measure belongs to the domain of attraction of a spectrally positive stable law. If conditioned to reach a high level and suitably scaled, this random walk converges in law to a nondecreasing Markov process which can be interpreted as a spectrally positive Lévy process conditioned not to overshoot level 1. 相似文献
128.
Shahriar Afandizadeh Mahmud Ameri Mohammad Hassan Mirabi Moghaddam 《Applied Mathematical Modelling》2011
In this paper, a new optimization method has been proposed for accident prediction non-linear models. This has been achieved by eliminating the Hessian matrix from the equation of optimal pace length in the gradient vector method. One advantage is that it is independent of the starting point in optimization processes and it provides convergence at the highest top as well. This method has been tested on an accident prediction model and its preference over the gradient vector method has been proven. 相似文献
129.
Shanshan Wang Luming Zhang Ran Fan 《Journal of Computational and Applied Mathematics》2011,235(8):1993-2005
In this paper, discrete-time orthogonal spline collocation schemes are proposed for the nonlinear Schrödinger equation with wave operator. These schemes are constructed by using orthogonal spline collocation approaches combined with finite difference methods. The conservative property, the convergence, and the stability of these methods are theoretically analyzed and also verified by extensive numerical experiments. In addition, some interesting phenomena which require further theoretical analysis are discussed numerically. 相似文献
130.
Ioannis K. Argyros 《Journal of Complexity》2011,27(1):39-54
We present a semilocal convergence theorem for Newton’s method (NM) on spaces with a convergence structure. Using our new idea of recurrent functions, we provide a tighter analysis, with weaker hypotheses than before and with the same computational cost as for Argyros (1996, 1997, 1997, 2007) [1], [2], [3] and [5], Meyer (1984, 1987, 1992) [13], [14] and [15]. Numerical examples are provided for solving equations in cases not covered before. 相似文献