共查询到20条相似文献,搜索用时 15 毫秒
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讨论变分不等式问题VIP(X,F),其中F是单调函数,约束集X为有界区域.利用摄动技术和一类光滑互补函数将问题等价转化为序列合两个参数的非线性方程组,然后据此建立VIP(X,F)的一个内点连续算法.分析和论证了方程组解的存在性和惟一性等重要性质,证明了算法很好的整体收敛性,最后对算法进行了初步的数值试验。 相似文献
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A. I. Pavlov 《Mathematical Notes》1999,66(4):442-450
The main result of the paper is as follows.Theorem. Suppose that G(z) is an entire function satisfying the following conditions: 1) the Taylor coefficients of the function
G(z) are nonnegative: 2) for some fixed C>0 and A>0 and for |z|>R0, the following inequality holds:
Further, suppose that for some fixed α>0 the deviation DN of the sequence xn={αn}, n=1, 2, ..., as N→∞ has the estimate DN=0(lnB N/N). Then if the function G(z) is not an identical constant and the inequality B+1<A holds, then the power series
converging in the disk |z|<1 cannot be analytically continued to the region |z|>1 across any arc of the circle |z|=1.
Translated fromMatematicheskie Zametki, Vol. 66, No. 4, pp. 540–550, October, 1999. 相似文献
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Prabir Daripa 《Journal of Computational and Applied Mathematics》1998,100(2):161-171
Some useful filtering techniques for computing approximate solutions of illposed are presented. Special attention is given to the role of smoothness of the filters and the choice of time-dependent parameters used in these filtering techniques. Smooth filters and proper choice of time-dependent parameters in these filtering techniques allow numerical construction of more accurate approximate solutions of illposed problems. In order to illustrate this and the filtering techniques, a severely illposed fourth-order nonlinear wave equation is numercally solved using a three time-level finite difference scheme. Numerical examples are given showing the merits of the filtering techniques. 相似文献
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In this study we present iterative regularization methods using rational approximations, in particular, Padé approximants, which work well for ill-posed problems. We prove that the (k, j)-Padé method is a convergent and order optimal iterative regularization method in using the discrepancy principle of Morozov. Furthermore, we present a hybrid Padé method, compare it with other well-known methods and found that it is faster than the Landweber method. It is worth mentioning that this study is a completion of the paper [A. Kirsche, C. Böckmann, Rational approximations for ill-conditioned equation systems, Appl. Math. Comput. 171 (2005) 385–397] where this method was treated to solve ill-conditioned equation systems. 相似文献
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This paper is concerned with the ill-posed Cauchy problem associated with a densely defined linear operator A in a Banach space. Our main result is that if −A is the generator of an analytic semigroup, then there exists a family of regularizing operators for such an ill-posed Cauchy problem by using the quasi-reversibility method, fractional powers and semigroups of linear operators. The applications to ill-posed partial differential equations are also given. 相似文献
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This paper presents results of some numerical experiments on the backward heat equation. Two quasi-reversibility techniques, explicit filtering and structural perturbation, to regularize the ill-posed backward heat equation have been used. In each of these techniques, two numerical methods, namely Euler and Crank-Nicolson (CN), have been used to advance the solution in time.Crank-Nicolson method is very counter-intuitive for solving the backward heat equation because the dispersion relation of the scheme for the backward heat equation has a singularity (unbounded growth) for a particular wave whose finite wave number depends on the numerical parameters. In comparison, the Euler method shows only catastrophic growth of relatively much shorter waves. Strikingly we find that use of smart filtering techniques with the CN method can give as good a result, if not better, as with the Euler method which is discussed in the main text. Performance of these regularization methods using these numerical schemes have been exemplified. 相似文献
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This paper is concerned with the final value problem associated with a linear operator A in a Banach space, where −A is the generator of a uniformly bounded analytic semigroup. Based on the deLaubenfels' functional calculus, we use new quasi-reversibility method, introduced by Boussetila and Rebbani recently, to form an approximate problem. We obtain some results in a Banach space similar to those in a Hilbert space. 相似文献
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For exact Newton method for solving monotone semidefinite complementarity problems (SDCP), one needs to exactly solve a linear system of equations at each iteration. For problems of large size, solving the linear system of equations exactly can be very expensive. In this paper, we propose a new inexact smoothing/continuation algorithm for solution of large-scale monotone SDCP. At each iteration the corresponding linear system of equations is solved only approximately. Under mild assumptions, the algorithm is shown to be both globally and superlinearly convergent. 相似文献
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Numerical differentiation is a classical ill-posed problem. In this paper, we propose a wavelet-Galerkin method for high order numerical differentiation. By an appropriate choice of the regularization parameter an order optimal stability estimate of Hölder type is obtained. Some numerical examples show that the method is effective and stable. 相似文献
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Frozen Landweber Iteration for Nonlinear Ill-Posed Problems 总被引:1,自引:0,他引:1
J. Xu B. Han L. Li 《应用数学学报(英文版)》2007,23(2):329-336
In this paper we propose a modification of the Landweber iteration termed frozen Landweberiteration for nonlinear ill-posed problems.A convergence analysis for this iteration is presented.The numericalperformance of this frozen Landweber iteration for a nonlinear Hammerstein integral equation is compared withthat of the Landweber iteration.We obtain a shorter running time of the frozen Landweber iteration based onthe same convergence accuracy. 相似文献
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This paper discusses the problem of determining an unknown source which depends only on one variable in two-dimensional Poisson equation from one supplementary temperature measurement at an internal point. The problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. The regularization solution is obtained by the modified regularization method. For the regularization solution, the Hölder type stability estimate between the regularization solution and the exact solution is given. Numerical results are presented to illustrate the accuracy and efficiency of this method. 相似文献
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M.P. Rajan 《Journal of Mathematical Analysis and Applications》2006,313(2):654-677
In this paper, we consider a finite-dimensional approximation scheme combined with Tikhonov regularization for solving ill-posed problems. Error estimates are obtained by an a priori parameter choice strategy and the results show that the amount of discrete information required for solving the problem is far less than the traditional finite-dimensional approach. 相似文献
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This paper deals with the inverse time problem for an axisymmetric heat equation. The problem is ill-posed. A modified Tikhonov regularization method is applied to formulate regularized solution which is stably convergent to the exact one. estimate between the approximate solution and exact technical inequality and improving a priori smoothness Meanwhile, a logarithmic-HSlder type error solution is obtained by introducing a rather assumption. 相似文献
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We show that the continuation method can be used to solve aweakly elliptic two-parameter eigenvalue problem. We generalizethe continuation method for a nonsymmetric eigenvalue problemAx = x by T. Y. Li, Z. Zeng and L. Cong (1992 SIAM J. Numer.Anal. 29, 229248) to two-parameter problems. 相似文献
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Discrepancy principles for Tikhonov regularization of ill-posed problems leading to optimal convergence rates 总被引:4,自引:0,他引:4
H. W. Engl 《Journal of Optimization Theory and Applications》1987,52(2):209-215
We propose a class ofa posteriori parameter choice strategies for Tikhonov regularization (including variants of Morozov's and Arcangeli's methods) that lead to optimal convergence rates toward the minimal-norm, least-squares solution of an ill-posed linear operator equation in the presence of noisy data. 相似文献
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This is the second in a series of three papers; the other two are “Summation Formulas, from Poisson and Voronoi to the Present” [Progr. Math. 220 (2004) 419-440] and “Automorphic Distributions, L-functions, and Voronoi Summation for GL(3)” (preprint). The first paper is primarily expository, while the third proves a Voronoi-style summation formula for the coefficients of a cusp form on . The present paper contains the distributional machinery used in the third paper for rigorously deriving the summation formula, and also for the proof of the GL(3)×GL(1) converse theorem given in the third paper. The primary concept studied is a notion of the order of vanishing of a distribution along a closed submanifold. Applications are given to the analytic continuation of Riemann's zeta function, degree 1 and degree 2 L-functions, the converse theorem for GL(2), and a characterization of the classical Mellin transform/inversion relations on functions with specified singularities. 相似文献
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Many industrial and engineering applications require numerically solving ill-posed problems. Regularization methods are employed to find approximate solutions of these problems. The choice of regularization parameters by numerical algorithms is one of the most important issues for the success of regularization methods. When we use some discrepancy principles to determine the regularization parameter, 相似文献
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Computation of control for a controlled partial differential equation is a di?cult task, especially when the control problem is ill posed. In this paper, we propose a method of computing the regularized control of a diffusion control system using Tikhonov regularization approach when the system is approximately controllable. The method proposed here for choosing regularization parameter guarantees the convergence of the proposed control. 相似文献