Lanczos based preconditioner for discrete ill-posed problems

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.

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