Regularization Of Two Kinds Of Nonhonmogeneous Ill-posed Problems

Ill-posed problems are very common in our life, such as resource exploration, spaceflight engineering, weather forcast, ocean engineering, iatrology imaging and so on. Because the instability of the ill-posed problems causes great trouble in numerical caculating, it is necessary to introduce regularization. There are already a lot of meth-ods of regularization existed, for example, Tikhonov regularization method, disperse method, projection method, semi-group method, Fourier method, wavelet method, QR method.One dimension homogeneous backward Cauchy problem is a typical kind of ill-posed problems, in which A is unbounded adjoint operator in Hilbert space H and-A generates a compact contraction semi-group. There is sizeable literature on this kind of problem, and many satisfactory results are obtaned. However, There is less research on the case of nonhomogeneous,2 dimension and multi-dimension, which is just this thesis going to consider.This thesis will discuss two problems in Hilbert space:nonhomogeneous backward heat equation in rectangle region and nonhomogeneous backward Cauchy problem. Through regularizing them by using QR method and QBV method, the thesis obtains corresponding error estimate. numerical examples are given at last.