A Density Matrix-based Algorithm for Solving Eigenvalue Problems

摘要

A new numerical algorithm for solving the symmetric eigenvalue problem ispresented. The technique deviates fundamentally from the traditional Krylovsubspace iteration based techniques (Arnoldi and Lanczos algorithms) or otherDavidson-Jacobi techniques, and takes its inspiration from the contourintegration and density matrix representation in quantum mechanics. It will beshown that this new algorithm - named FEAST - exhibits high efficiency,robustness, accuracy and scalability on parallel architectures. Examples fromelectronic structure calculations of Carbon nanotubes (CNT) are presented, andnumerical performances and capabilities are discussed.