| Ill-posed Cauchy problems have a wealth of background, since the sixties of last century much of the attention has formed a number of theories and methods. The theories and methods are also widely used in science and engineering fields, such as weather forecasting, remote sensing, medical imaging, marine engineering and so on.In this paper, let H is a separable Hilbert space, we consider the following backward Cauchy problem where g e H, A is a positive self-adjoint operator and—A generates a Co semi-group on H.In general, such problems are unstable, and thus are ill-posed. It is necessary to introduce regularization method. There are already a variety of regularization method existed, but there is no literature to make systematically a comparison for the specific effects of these methods.This thesis is to compare the QBV method introduced by Denche, QR method of Lattes-Lions and Gajewski-Zaccharias QR method with the mehhods from [23,24] introduced by Ames, etc., where [23] is Tikhonov's method of promoting, [24] is the quasi-boundary value method of Clark. At last, numerical examples are given.The main conclusion is that: under certain constraints, the inversion effect of QBV method is better than the method of [23]; and compared with the method of [24], the inver-sion effect of [24] method is better than QBV method.For the QR method of Latter-Lions, when the regular solution is only a finite time, the QR method of Latter-Lions is better than the method of literature [23,24] in inversion effect; when the regular solution with unlimited items, the inversion effect of [23,24] method is better.For the QR method of Gajewski-Zaccharias, when the eigenvalue is small and inverse time t is small, Gajewski-Zaccharias is better than [23]; when the inversion time t close to the end time, the inversion effect of [23] is relatively good. On the other hand, compared with the method of literature [24], the inversion effect of Gajewski-Zaccharias's QR method is better. |
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