{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,12]],"date-time":"2026-09-12T02:52:50Z","timestamp":1789181570052,"version":"build-2803163510"},"reference-count":39,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/100006132","name":"Office of Science","doi-asserted-by":"publisher","award":["DE-AC02-05CH11231"],"award-info":[{"award-number":["DE-AC02-05CH11231"]}],"id":[{"id":"10.13039\/100006132","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>We present a new structure preserving Lanczos algorithm for approximating the optical absorption spectrum in the context of solving the 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.<\/jats:p>","DOI":"10.1137\/16m1102641","type":"journal-article","created":{"date-parts":[[2018,4,24]],"date-time":"2018-04-24T14:17:34Z","timestamp":1524579454000},"page":"683-711","source":"Crossref","is-referenced-by-count":21,"title":["A Structure Preserving Lanczos Algorithm for Computing the Optical Absorption Spectrum"],"prefix":"10.1137","volume":"39","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4914-7666","authenticated-orcid":true,"given":"Meiyue","family":"Shao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Felipe H.","family":"da Jornada","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lin","family":"Lin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chao","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jack","family":"Deslippe","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Steven G.","family":"Louie","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,4,24]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/110838972"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1088\/0953-8984\/22\/7\/074204"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2016.12.047"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(96)00524-1"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2018.01.014"},{"key":"atypb6","unstructured":"P. Benner and A. Salam,\n                      The symplectic Lanczos process for Hamiltonian-positive matrices\n                      , preprint, 2011."},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1021\/acs.jctc.5b00887"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.78.382"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2011.12.006"},{"key":"atypb10","first-page":"105","author":"Golub G. H.","year":"1994","journal-title":"UK"},{"key":"atypb11","doi-asserted-by":"crossref","unstructured":"G. H. Golub and G. Meurant,\n                      Matrices, Moments and Quadrature with Applications\n                      , Princeton University Press, Princeton, NJ, 2010.","DOI":"10.1515\/9781400833887"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1021\/nl803717g"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1016\/j.commatsci.2011.02.021"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1016\/S0081-1947(08)60505-6"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2011.04.020"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1039\/c3cs00007a"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.85.035316"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.111.216805"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1007\/s10543-015-0592-7"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1063\/1.3677667"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1063\/1.2899649"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1063\/1.3494540"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.85.045116"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1021\/ct5000956"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.62.4927"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.84.1232"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2015.09.036"},{"key":"atypb28","unstructured":"M. Shao and C. Yang,\n                      BSEPACK User's Guide\n                      , arXiv:1612.07848, 2016."},{"key":"atypb29","doi-asserted-by":"crossref","unstructured":"M. Shao and C. Yang,\n                      Properties of definite Bethe-Salpeter eigenvalue problems\n                      , in Eigenvalue Problems: Algorithms, Software and Applications, in Petascale Computing, T. Sakurai, S.L. Zhang, T. Imamura, Y. Yamamoto, Y. Kuramashi, and T. Hoshi, eds., Lect. Notes Comput. Sci. Eng. 117, Springer-Verlag, Berlin, 2017, pp. 91-105,https:\/\/doi.org\/10.1007\/978-3-319-62426-6_7.","DOI":"10.1007\/978-3-319-62426-6_7"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-07-01975-8"},{"key":"atypb31","doi-asserted-by":"crossref","unstructured":"G. Strinati,\n                      Application of the Green's functions method to the study of the optical properties of semiconductors\n                      , La Rivista del Nuovo Cimento, 11 (1988), pp. 1-86.","DOI":"10.1007\/BF02725962"},{"key":"atypb32","first-page":"449","volume":"9","author":"Tamm I. Y.","year":"1945","journal-title":"J. Phys. 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