Preconditioned Lanczos algorithms

Matrix Spectroscopy The Preconditioned Green-Function Block Lanczos Algorithm. 

However, a Cl hamiltonian matrix have eigenvalues spread out in a very wide range, and this reduces the value of the Lanczos algorithm for Cl purposes. Attempts have been made to precondition the Lanczos procedure, such that the iterations are governed by a clustered matrix while at the same time a stable subspace of the original matrix is constructed. The success of such a scheme has yet to be demonstrated. 

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