Iterative solution of regularization to ill-conditioned problems in geodesy and geophysics

In geodesy and geophysics, many large-scale over-determined linear equations need to be solved which are often ill-conditioned. When the conjugate gradient method is used, their ill-conditioned effects to the solutions must be overcome. By regularization ideas, the conjugate gradient method is improved. Firstly, by constructing the interference source vector, a new equation is derived with ill-condition diminished greatly, which has the same solution to the original normal equation. Then the new equation is solved by conjugate gradient method. Finally, the effectiveness of the new method is verified by some numerical experiments of airborne gravity downward to the earth surface. In the numerical experiments, the new method is compared with LS, CG and Tikhonov methods, and its accuracy is the highest.