Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download An eigenvalue problem in electronic structure calculations and its
Document related concepts
Knapsack problem wikipedia , lookup
Exact cover wikipedia , lookup
Perturbation theory wikipedia , lookup
Computational fluid dynamics wikipedia , lookup
Computational complexity theory wikipedia , lookup
Non-negative matrix factorization wikipedia , lookup
Travelling salesman problem wikipedia , lookup
Computational chemistry wikipedia , lookup
Eigenvalues and eigenvectors wikipedia , lookup
Inverse problem wikipedia , lookup
Computational electromagnetics wikipedia , lookup
Transcript
An eigenvalue problem in electronic structure calculations and its solution by spectrum slicing Dongjin Lee† , Takeo Hoshi‡ , Yuto Miyatake† , Tomohiro Sogabe† , and Shao-Liang Zhang† † ‡ Graduate School of Engineering, Nagoya University Department of Applied Mathematics and Physics, Tottori University A generalized Hermitian eigenvalue problem in electronic structure calculations is studied. In particular, we are interested in a small number of eigenpairs which are in close relation with several material properties. The eigenpairs of interest can be formally expressed as follows: for a given index k, the k-th smallest eigenpair. A numerical approach to the problem, which is built upon the spectrum slicing framework of the bisection and utilizes the matrix inertia and the Lanczos method, is presented. Numerical results with the matrix size up to one million are reported.
