Truncated Least-squares Least-norm Solutions by Applying the QR Decompositions Twice

摘要

We investigate the numerical method applied to ill-posed problems including the Fredholm integral equation of the first kind. In place of the truncated least-square least-norm solution (TLSLNS) which applies the QR decomposition three times, we propose a TLSLNS which applies the QR decomposition only twice. The new method is numerically stable, and numerical experiments show that the method gives results of similar accuracy compared to the truncated singular value decomposition method.