The optimal approximations for solving linear ill-posed problems (Q5938582)

Recently, investigations on the information complexity have received a lot of attention in solving various problems. In this study, by complexity we mean the minimal amount of discrete information required to guarantee a fixed accuracy of an approximated solution to the problem.NEWLINENEWLINENEWLINEThe goal of the paper is the construction of some new projection schemes for the discretization of ill-posed problems, which are optimal on several classes of equations of the first kind. In particular, the author establishes the unexpected effect that the use of selfadjoint approximating operators in the discretization of equations with selfadjoint operators is generally not optimal in the sense of volume of used discrete information.