本文将求解不适定问题的Tikhonov正则化方法推广到带有多个正则参数的情形,对于泛函 M~((α_1,…,α_N))[Z,v,A]=ρ~2(AZ,v)+α_1Ω_1[Z]+…+α_NΩ_N[Z] 证明了对任意给定的一组正则参数α_i>0(i=1,2,…,N),其泛函的极小元存在,以及在正则参数的选取满足一定的条件下,泛函的极小元对数据的扰动具有连续依赖性。 In this paper, we generalize the Tikhonov regularization method for solving ill-posed problems to a case with multiple regular parameters. For the functional M ~ (α_1, ..., α_N) [Z, v, A] = ρ ~ 2 v) + α_1Ω_1 [Z] + ... + α_NΩ_N [Z] Prove that for any given set of regular parameters α_i> 0 (i = 1,2, ..., N) Under the condition that the regular parameters are chosen to satisfy certain conditions, the minimal element of the functional has a continuous dependence on the data perturbation.