Lanczos based preconditioner for discrete ill-posed problems

摘要

In this paper we use the Lanczos process for preconditioning discrete ill-posed problems. We show that by few steps of this process one can obtain a well qualified and efficient preconditioner. This is a general method in the sense that it is not limited only to special structured matrices and the matrix-vector multiplications can be carried out in O(n) operations. Also even in problems with structured matrices this preconditioner performs more efficiently than the circulant and Kronecker product approximate preconditioners.[PUBLICATION ABSTRACT]