# A structure preserving Lanczos algorithm for computing the optical absorption spectrum

## Abstract

We present a new structure preserving Lanczos algorithm for approximating the optical absorption spectrum in the context of solving full Bethe-Salpeter equation without Tamm-Dancoff approximation. The new algorithm is based on a structure preserving Lanczos procedure, which exploits the special block structure of Bethe-Salpeter Hamiltonian matrices. A recently developed technique of generalized averaged Gauss quadrature is incorporated to accelerate the convergence. We also establish the connection between our structure preserving Lanczos procedure with several existing Lanczos procedures developed in different contexts. Numerical examples are presented to demonstrate the effectiveness of our Lanczos algorithm.

- Authors:

- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Div.
- Univ. of California, Berkeley, CA (United States). Dept. of Physics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Materials Science Div.
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Div.; Univ. of California, Berkeley, CA (United States). Dept. of Mathematics
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

- OSTI Identifier:
- 1398473

- Grant/Contract Number:
- AC02-05CH11231

- Resource Type:
- Journal Article: Accepted Manuscript

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING

### Citation Formats

```
Shao, Meiyue, Jornada, Felipe H. da, Lin, Lin, Yang, Chao, Deslippe, Jack, and Louie, Steven G..
```*A structure preserving Lanczos algorithm for computing the optical absorption spectrum*. United States: N. p., 2016.
Web. doi:10.1137/16M1102641.

```
Shao, Meiyue, Jornada, Felipe H. da, Lin, Lin, Yang, Chao, Deslippe, Jack, & Louie, Steven G..
```*A structure preserving Lanczos algorithm for computing the optical absorption spectrum*. United States. doi:10.1137/16M1102641.

```
Shao, Meiyue, Jornada, Felipe H. da, Lin, Lin, Yang, Chao, Deslippe, Jack, and Louie, Steven G.. Wed .
"A structure preserving Lanczos algorithm for computing the optical absorption spectrum". United States. doi:10.1137/16M1102641. https://www.osti.gov/servlets/purl/1398473.
```

```
@article{osti_1398473,
```

title = {A structure preserving Lanczos algorithm for computing the optical absorption spectrum},

author = {Shao, Meiyue and Jornada, Felipe H. da and Lin, Lin and Yang, Chao and Deslippe, Jack and Louie, Steven G.},

abstractNote = {We present a new structure preserving Lanczos algorithm for approximating the optical absorption spectrum in the context of solving full Bethe-Salpeter equation without Tamm-Dancoff approximation. The new algorithm is based on a structure preserving Lanczos procedure, which exploits the special block structure of Bethe-Salpeter Hamiltonian matrices. A recently developed technique of generalized averaged Gauss quadrature is incorporated to accelerate the convergence. We also establish the connection between our structure preserving Lanczos procedure with several existing Lanczos procedures developed in different contexts. Numerical examples are presented to demonstrate the effectiveness of our Lanczos algorithm.},

doi = {10.1137/16M1102641},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Wed Nov 16 00:00:00 EST 2016},

month = {Wed Nov 16 00:00:00 EST 2016}

}

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