{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T13:16:43Z","timestamp":1788268603899,"version":"build-2803163510"},"reference-count":33,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>The shift-invert Arnoldi method is employed to generate an orthonormal basis from the Krylov subspace corresponding to a real Toeplitz matrix and an initial vector. The vectors and recurrence coefficients produced by this method are exploited to approximate the Toeplitz matrix exponential. Toeplitz matrix inversion formula and rapid Toeplitz matrix-vector multiplications are utilized to lower the computational costs. For convergence analysis, a sufficient condition is established to guarantee that the error bound is independent of the norm of the matrix. Numerical results are given to demonstrate the efficiency of the method.<\/jats:p>","DOI":"10.1137\/090758064","type":"journal-article","created":{"date-parts":[[2010,3,3]],"date-time":"2010-03-03T18:09:18Z","timestamp":1267639758000},"page":"774-792","source":"Crossref","is-referenced-by-count":49,"title":["Shift-Invert Arnoldi Approximation to the Toeplitz Matrix Exponential"],"prefix":"10.1137","volume":"32","author":[{"given":"Spike T.","family":"Lee","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hong-Kui","family":"Pang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hai-Wei","family":"Sun","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,3,3]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(01)00003-0"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/0609005"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst,\n                      Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide\n                      , SIAM, Philadelphia, 2000.","DOI":"10.1137\/1.9780898719581"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1099-1506(200001\/02)7:1<27::AID-NLA185>3.0.CO;2-4"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"R. Chan and X. Jin,\n                      An Introduction to Iterative Toeplitz Solvers\n                      , SIAM, Philadelphia, 2007.","DOI":"10.1137\/1.9780898718850"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144594276474"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/0730062"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/070688924"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1137\/050633846"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/040605461"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/070684598"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1137\/0913071"},{"key":"R13","first-page":"201","volume":"2","author":"Gohberg I.","year":"1972","journal-title":"Mat. Issled.","ISSN":"https:\/\/id.crossref.org\/issn\/0542-9994","issn-type":"print"},{"key":"R14","unstructured":"G. Golub and C. Van Loan,\n                      Matrix Computations\n                      , 3rd ed., The John Hopkins University Press, Baltimore, 1996."},{"key":"R15","doi-asserted-by":"crossref","unstructured":"G. Heinig and K. Rost,\n                      Algebraic Methods for Toeplitz-Like Matrices and Operators\n                      , Birkh\u00e4user Verlag, Basel, 1984.","DOI":"10.1515\/9783112529003"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1137\/04061101X"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142995280572"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1137\/05062590"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1016\/0304-405X(76)90022-2"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1137\/1020098"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1137\/S00361445024180"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1002\/nla.532"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(00)00261-2"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1023\/B:BITN.0000046805.27551.3b"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827500378155"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1137\/060672856"},{"key":"R27","unstructured":"R. Rockafellar,\n                      Convex Analysis\n                      , Princeton University Press, Princeton, NJ, 1970."},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1137\/0729014"},{"key":"R29","doi-asserted-by":"crossref","unstructured":"Y. Saad,\n                      Iterative Methods for Sparse Linear Systems\n                      , 2nd ed., SIAM, Philadelphia, 2003.","DOI":"10.1137\/1.9780898718003"},{"key":"R30","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(99)00104-1"},{"key":"R31","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827502406415"},{"key":"R32","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2007.07.005"},{"key":"R33","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(97)00308-X"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/090758064","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:50:16Z","timestamp":1787334616000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/090758064"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":33,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/090758064"],"URL":"https:\/\/doi.org\/10.1137\/090758064","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}