Perturbed Projection Methods For M-P Inverses Of Integral Operators

In this paper,for a specific integral operator K,the combination of the least squares projection method with the stable perturbation is presented to solve the essential issues of format perturbation in the computational scheme of operator equations and their perturbation systems.First,we utilize the operator K to derive the first kind integral equation Kx = y and shows that the norm convergence of the projection approximation format {Kn+} of its approximate solution K+ can withstand stable perturbation.Then the operator K leads to the second kind integral equation T?:=(?I-K)(? = f and we illustrate that when ? is the eigenvalue of the operator K,the projection approximation format {Tn+} of its approximate solution t failed to withstand stable perturbation by-using the counterexample(the conclusion is totally opposite when ? is not the eigenvalue of the operator K).