We study Chebyshev filter diagonalization as a tool for the computation ofmany interior eigenvalues of very large sparse symmetric matrices. In thistechnique the subspace projection onto the target space of wanted eigenvectorsis approximated with filter polynomials obtained from Chebyshev expansions ofwindow functions. After the discussion of the conceptual foundations ofChebyshev filter diagonalization we analyze the impact of the choice of thedamping kernel, search space size, and filter polynomial degree on thecomputational accuracy and effort, before we describe the necessary stepstowards a parallel high-performance implementation. Because Chebyshev filterdiagonalization avoids the need for matrix inversion it can deal with matricesand problem sizes that are presently not accessible with rational functionmethods based on direct or iterative linear solvers. To demonstrate thepotential of Chebyshev filter diagonalization for large-scale problems of thiskind we include as an example the computation of the $10^2$ innermosteigenpairs of a topological insulator matrix with dimension $10^9$ derived fromquantum physics applications.
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