{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T20:58:38Z","timestamp":1776805118812,"version":"3.51.2"},"reference-count":33,"publisher":"American Mathematical Society (AMS)","issue":"319","license":[{"start":{"date-parts":[[2020,1,9]],"date-time":"2020-01-09T00:00:00Z","timestamp":1578528000000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100001779","name":"Monash University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001779","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004663","name":"Ministry of Science and Technology, Taiwan","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004663","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    The discretized Bethe-Salpeter eigenvalue problem arises in the Green\u2019s function evaluation in many body physics and quantum chemistry. Discretization leads to a matrix eigenvalue problem for\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper H element-of double-struck upper C Superscript 2 n times 2 n\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>H<\/mml:mi>\n                            <mml:mo>\n                              \u2208\n                              \n                            <\/mml:mo>\n                            <mml:msup>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi mathvariant=\"double-struck\">C<\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mn>2<\/mml:mn>\n                                <mml:mi>n<\/mml:mi>\n                                <mml:mo>\n                                  \u00d7\n                                  \n                                <\/mml:mo>\n                                <mml:mn>2<\/mml:mn>\n                                <mml:mi>n<\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">H \\in \\mathbb {C}^{2n \\times 2n}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    with a Hamiltonian-like structure. After an appropriate transformation of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper H\">\n                        <mml:semantics>\n                          <mml:mi>H<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">H<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    to a standard symplectic form, the structure-preserving doubling algorithm, originally for algebraic Riccati equations, is extended for the discretized Bethe-Salpeter eigenvalue problem. Potential breakdowns of the algorithm, due to the ill condition or singularity of certain matrices, can be avoided with a double-Cayley transform or a three-recursion remedy. A detailed convergence analysis is conducted for the proposed algorithm, especially on the benign effects of the double-Cayley transform. Numerical results are presented to demonstrate the efficiency and the structure-preserving nature of the algorithm.\n                  <\/p>","DOI":"10.1090\/mcom\/3398","type":"journal-article","created":{"date-parts":[[2019,1,9]],"date-time":"2019-01-09T12:38:25Z","timestamp":1547037505000},"page":"2325-2350","source":"Crossref","is-referenced-by-count":3,"title":["Doubling algorithm for the discretized Bethe-Salpeter eigenvalue problem"],"prefix":"10.1090","volume":"88","author":[{"given":"Zhen-Chen","family":"Guo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eric","family":"Chu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wen-Wei","family":"Lin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2019,1,9]]},"reference":[{"issue":"4","key":"1","doi-asserted-by":"publisher","first-page":"1075","DOI":"10.1137\/110838960","article-title":"Minimization principles for the linear response eigenvalue problem I: Theory","volume":"33","author":"Bai, Zhaojun","year":"2012","journal-title":"SIAM J. 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