A Density Matrix-based Algorithm for Solving Eigenvalue Problems

By Eric Polizzi. arXiv.org, 2009

379 citations recorded by the source corpus.

A new numerical algorithm for solving the symmetric eigenvalue problem is presented. The technique deviates fundamentally from the traditional Krylov subspace iteration based techniques (Arnoldi and Lanczos algorithms) or other Davidson-Jacobi techniques, and takes its inspiration from the contour integration and density matrix representation in quantum mechanics. It will be shown that this new algorithm - named FEAST - exhibits high efficiency, robustness, accuracy and scalability on parallel architectures. Examples from electronic structure calculations of Carbon nanotubes (CNT) are presented, and numerical performances and capabilities are discussed.

Subfields: Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/c4bde15f96fba8c20117695dc96062b2271795e5