The Application Of The Tikhonov Regularized Method With Constraints

Because of substantive involvement of additional assumption on the solution space, the constrained inverse problem is more difficult to deal with and it can not be solved by unconstrained regularization without modification. To get so-called C-best-approximate solutin on a certain constrained set C, we employ the constrained regularization method to solve Fredholm integral equation of the first kind with nonnegative constraints.The emphasis on the applications of constrained regularization method is the identification of weight density distribution of hanging cable and rotating shaft, inversion of particle size distribution from light scattering data, the reconstruction of the atomatic radial distribution in EXAFS spec-troscopy. Meanwhile, the numerical tests are also made, the theoretic analysis and numerical results of the constrained inverse problems show that results obtained from the constrained regularization is better and more reasonable than that from the unconstrained regularization.