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5. Conclusions

In this work we have proposed an iterative conjugate gradient method to obtain the lowest few eigenvalues and corresponding eigenvectors of the generalized eigenvalue problem $H x = \varepsilon S x $, which exhibits linear convergence. A preconditioning scheme which uses the kinetic energy matrix is introduced to improve the convergence of the solutions. The scheme is controlled by a single parameter whose optimal value may be chosen automatically.

Peter Haynes