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arXiv · 0901.2665

A Density Matrix-based Algorithm for Solving Eigenvalue Problems

Eric Polizzi
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Abstract

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.

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Eric Polizzi. 2009-01-17. A Density Matrix-based Algorithm for Solving Eigenvalue Problems. https://doi.org/10.1103/physrevb.79.115112

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