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We present a combination method based on orignal version of Davidsonalgorithm for extracting few of the lowest eigenvalues and eigenvectors of asparse symmetric Hamiltonian matrix and the simplest version of Lanczostechnique for obtaining a tridiagonal representation of the Hamiltonian tocompute the continued fraction expansion of the Green's function at a very lowtemperature. We compare the Davidson$+$Lanczos method with the fulldiagonalization on a one-band Hubbard model on a Bethe lattice ofinfinite-coordination using dynamical mean field theory.

A Davidson-Lanczos iteration method for computation of  continued-fraction expansion of the Green's function at very low  temperatures: Applications to the dynamical mean field theory