A Comparison of Numerical Implementations of the Eigenstate Expansion Method for Quantum Molecular Dynamics Simulations
نویسندگان
چکیده
We investigate the efficient computation of a few of the lowest eigenvalues of a symmetric eigenvalue problem occurring in quantum dynamical molecular simulations. The large sparse system of order n is highly structured such that its multiplication with a vector costs O(n logn) floating point operations only. We compare a number of eigensolvers: subspace iteration, two variants of the restarted Lanczos algorithm, among them ARPACK, the Jacobi-Davidson algorithm and the classical algorithms from LAPACK for full matrices. Some of them are applied with a shift-and-invert spectral transformation. The arising systems of equations are solved by the preconditioned conjugate gradient method for which new efficient ADI-type preconditioners are proposed and analyzed.
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