An a posteriori wavelet method for solving two kinds of ill-posed problems

ABSTRACTThe wavelet method based on the Meyer wavelet function and scaling function is a rather effective regularization method for solving some ill-posed problems. Recently, there are many works on this method limited to the a priori choice rule. The typical paper [H. Cheng and C.L. Fu, Wavelets and numerical pseudodifferential operator, Appl. Math. Model. 40 (2016), pp. 1776–1787] has systematically considered the a priori choice rule in the framework of the pseudodifferential operator (ΨDO). In this paper, we will systematically consider the a posteriori choice rule for two kinds of ill-posed problems in the framework of the ΨDO, and construct the convergence error estimates between the exact solution and its regularized approximation.