A New Method for Linear Ill-Posed Problems: Iteration Method by Rectifying Eigenvalue

Abstract

In order to overcome the weaknesses of Regularization Method for linear ill-posed problem, the authors suggest a new method named Iteration Method by Rectifying Eigenvalue (IMRE) in this paper. Firstly, the rigorous theoretical proofs that IMRE can achieve convergent and unbiased solution are given. Then an effective method called L-Curve method is introduced to determine parameter α in IMRE. Thirdly, a computing program is designed. Finally an example is given to testify the advantages of IMRE by the above program.