Multilevel algorithms for ill-posed problems
While the theory of multilevel algorithms is well developed for well- posed problems, this is one of the first papers studying multilevel algorithms for (linear) ill-posed problems. The author considers the weak form of Tikhonov regularization on the (finite dimensional) range space, constructs a multilevel operator on this finite dimensional space and gives error estimates with respect to the bilinear form corresponding to Tikhonov regularization. This multilevel operator is then used as a preconditioner for the Landweber and the conjugate gradient methods. The abstract results are carefully illustrated by numerical examples, namely the first kind integral equations corresponding to computing the second derivative and to the sideways heat equation, respectively.
scientific article; zbMATH DE number 118291
scientific article