The Mollification Method And Its Application

This thesis is to recommend a important class of Regularized strategies for solving inverse problems- Mollifier Method. It anaysises the consistency , numerical stability and error estimates of Mollified solution.Similar to Tikhonov Regularization , a discrepancy principle for selecting the mol-lifier parameter is proven and applications to numerical differentiation and numerical inversion of Abel Transform and also given.Theoretical analysis and numerical testing results indicate that the Mollifier Method with its flexibility ,stability and practicality ,provides a new effective tool for numerically solving inverse problems.