期刊
COMPUTING AND VISUALIZATION IN SCIENCE
卷 11, 期 4-6, 页码 259-271出版社
SPRINGER
DOI: 10.1007/s00791-008-0097-x
关键词
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In the present paper we discuss efficient rank-structured tensor approximation methods for 3D integral transforms representing the Green iterations for the Kohn-Sham equation. We analyse the local convergence of the Newton iteration to solve the Green's function integral formulation of the Kohn-Sham model in electronic structure calculations. We prove the low-separation rank approximations for the arising discrete convolving kernels given by the Coulomb and Yukawa potentials 1/|x|, and e(-lambda| x|)/|x|, respectively, with x. Rd. Complexity analysis of the nonlinear iteration with truncation to the fixed Kronecker tensor-product format is presented. Our method has linear scaling in the univariate problem size. Numerical illustrations demo-strate uniform exponential convergence of tensor approximations in the orthogonal Tucker and canonical formats.
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