Efficient low-order scaling method for large-scale electronic structure calculations with localized basis functions

Physical Review B - Condensed Matter and Materials Physics

Volumn 82, Issue 7, 2010, Pages

  Ozaki, Taisuke ^a  

^a JAPAN ADVANCED INSTITUTE OF SCIENCE AND TECHNOLOGY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77957575829     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.82.075131     Document Type: Article

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62. ) 2 with the analytically evaluated coefficients as initial values. We find that the coefficients refined by the minimization are much more accurate than the analytic ones for serious cases, and that the refinement is quite effective to avoid the numerical instability.
63. It is noted that the recurrence formula derived by Lin allows us to compute selected elements in O (N 2) operations for 3D systems (Ref.), which is superior to our recurrence formulas. However, the size of separators in their way for the nested dissection can be larger than that of our separators especially for the case that basis functions overlap with a number of other basis functions like in the PAO basis functions, which leads to a large prefactor for the computational cost in spite of the lower scaling. Also, the comparison with the algorithm by Takahashi (Ref.) and Erisman and Tinney (Ref.) will be in a future work.
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