Application of Wavelet Shrinkage to Laplace Equation
Weifang Wang, Jinru Wang · Journal of Tangshan Teachers College · 2009
The Cauchy problem for the Laplace equation was considered in terms of the ill-posed operator eqation, with a given noisy right hand side. For a reconstruction of the solution from inaccurate data, the dual least squares method generated by the family of Shannon wavelet subspaces was applied. An explicit relation between the truncation level of the wavelet expansion was given, the convergence results including error estimate were obtained. According to the reference, the error estimate was order optimal. Next, a certain simple nonlinear modification of the method was investigated.