{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:24:33Z","timestamp":1787333073799,"version":"build-2736575974"},"reference-count":14,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/501100001822","name":"Austrian Academy of Sciences","doi-asserted-by":"publisher","award":["DOC Fellowship"],"award-info":[{"award-number":["DOC Fellowship"]}],"id":[{"id":"10.13039\/501100001822","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["MATFUN 267526"],"award-info":[{"award-number":["MATFUN 267526"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/I01912X\/1"],"award-info":[{"award-number":["EP\/I01912X\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>We derive a new algorithm for computing the action $f(A)V$ of the cosine, sine, hyperbolic cosine, and hyperbolic sine of a matrix $A$ on a matrix $V$, without first computing $f(A)$. The algorithm can compute $\\cos(A)V$ and $\\sin(A)V$ simultaneously, and likewise for $\\cosh(A)V$ and $\\sinh(A)V$, and it uses only real arithmetic when $A$ is real. The algorithm exploits an existing algorithm expmv of Al-Mohy and Higham for $\\mathrm{e}^AV$ and its underlying backward error analysis. Our experiments show that the new algorithm performs in a forward stable manner and is generally significantly faster than alternatives based on multiple invocations of expmv through formulas such as $\\cos(A)V = (\\mathrm{e}^{\\mathrm{i}A}V + \\mathrm{e}^{\\mathrm{-i}A}V)\/2$.<\/jats:p>","DOI":"10.1137\/16m1084225","type":"journal-article","created":{"date-parts":[[2017,4,20]],"date-time":"2017-04-20T11:56:25Z","timestamp":1492689385000},"page":"A613-A627","source":"Crossref","is-referenced-by-count":9,"title":["Computing the Action of Trigonometric and Hyperbolic Matrix Functions"],"prefix":"10.1137","volume":"39","author":[{"given":"Nicholas J.","family":"Higham","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter","family":"Kandolf","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,4,20]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/09074721X"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/100788860"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/140973979"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/15M1027620"},{"key":"atypb5","first-page":"1","volume":"38","author":"Davis T. A.","year":"2011","journal-title":"ACM Trans. Math. Software"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1145\/2491491.2491494"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.78.026102"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1007\/s10543-009-0236-x"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-005-8141-0"},{"key":"atypb10","volume-title":"MATLAB Guide","author":"Higham D. J.","year":"2017","edition":"3"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717778"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479899356080"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492910000048"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1145\/2365934.2365942"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/16M1084225","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:30:00Z","timestamp":1787329800000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/16M1084225"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1]]},"references-count":14,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["10.1137\/16M1084225"],"URL":"https:\/\/doi.org\/10.1137\/16m1084225","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1]]}}}