{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,13]],"date-time":"2023-09-13T18:27:19Z","timestamp":1694629639249},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2007,3,31]],"date-time":"2007-03-31T00:00:00Z","timestamp":1175299200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2007,3,31]],"date-time":"2007-03-31T00:00:00Z","timestamp":1175299200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2007,5]]},"DOI":"10.1007\/s00211-007-0072-3","type":"journal-article","created":{"date-parts":[[2007,3,30]],"date-time":"2007-03-30T09:47:43Z","timestamp":1175248063000},"page":"511-528","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Averaging operators for exponential splittings"],"prefix":"10.1007","volume":"106","author":[{"given":"Marko","family":"Huhtanen","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2007,3,31]]},"reference":[{"issue":"1","key":"72_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1023\/B:FAIA.0000024863.06462.68","volume":"38","author":"V.I. Arnold","year":"2004","unstructured":"Arnold V.I. (2004). Fermat dynamics, matrix arithmetics, finite circles and the finite Lobachevsky planes. Funct. Anal. Appl. 38(1): 1\u201313","journal-title":"Funct. Anal. Appl."},{"issue":"1","key":"72_CR2","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1080\/03081088308817542","volume":"14","author":"S. Barnett","year":"1983","unstructured":"Barnett S. and Gover M.J. (1983). Some extensions of Hankel and Toeplitz matrices. Linear Multilinear Algebra 14(1): 45\u201365","journal-title":"Linear Multilinear Algebra"},{"key":"72_CR3","volume-title":"Matrix Analysis Graduate Texts in Mathematics, 169","author":"R. Bhatia","year":"1997","unstructured":"Bhatia R. (1997). Matrix Analysis Graduate Texts in Mathematics, 169. Springer, New York"},{"issue":"7","key":"72_CR4","doi-asserted-by":"publisher","first-page":"602","DOI":"10.2307\/2589115","volume":"107","author":"R. Bhatia","year":"2000","unstructured":"Bhatia R. (2000). Pinching, trimming, truncating and averaging of matrices. Am. Math. Mon. 107(7): 602\u2013608","journal-title":"Am. Math. Mon."},{"issue":"1","key":"72_CR5","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1080\/03081080290011674","volume":"50","author":"R. Bhatia","year":"2002","unstructured":"Bhatia R., Kahan W. and Li R.-C. (2002). Pinchings and norms of scaled triangular matrices. Linear Multilinear Algebra 50(1): 15\u201321","journal-title":"Linear Multilinear Algebra"},{"key":"72_CR6","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1137\/S0036144594276474","volume":"38","author":"R.N. Chan","year":"1996","unstructured":"Chan R.N. and Ng M.K. (1996). Conjugate gradient methods for Toeplitz systems. SIAM Rev. 38: 427\u2013482","journal-title":"SIAM Rev."},{"key":"72_CR7","doi-asserted-by":"crossref","unstructured":"Davidson, K.: C\n                           *-Algebras by Example. Fields Institute Monograph Series, vol. 6 (1996)","DOI":"10.1090\/fim\/006"},{"issue":"8","key":"72_CR8","doi-asserted-by":"publisher","first-page":"655","DOI":"10.2307\/4145039","volume":"111","author":"O. Holtz","year":"2004","unstructured":"Holtz O., Mehrmann V. and Schneider H. (2004). Potter, Wielandt, and Drazin on the matrix equation AB\u00a0=\u00a0\u03c9 BA: new answers to old questions. Am. Math. Mon. 111(8): 655\u2013667","journal-title":"Am. Math. Mon."},{"key":"72_CR9","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1007\/PL00005406","volume":"86","author":"M. Huhtanen","year":"2000","unstructured":"Huhtanen M. and Nevanlinna O. (2000). Minimal decompositions and iterative methods. Numer. Math. 86: 257\u2013281","journal-title":"Numer. Math."},{"key":"72_CR10","doi-asserted-by":"publisher","first-page":"735","DOI":"10.1023\/A:1022396519656","volume":"40","author":"T. Jahnke","year":"2000","unstructured":"Jahnke T. and Lubich C. (2000). Error bounds for exponential operator splittings. BIT 40: 735\u2013744","journal-title":"BIT"},{"key":"72_CR11","doi-asserted-by":"crossref","first-page":"706","DOI":"10.1137\/S0895479896312560","volume":"26","author":"T. Kailath","year":"2005","unstructured":"Kailath, T., Olshevsky, V.: Displacement structure approach to discrete-trigonometric-transform based preconditioners of G. Strang type and of T. Chan type. SIAM J. Matrix Anal. Appl. 26, 706\u2013734 (2005)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"72_CR12","doi-asserted-by":"publisher","first-page":"576","DOI":"10.1016\/j.jcp.2003.10.011","volume":"195","author":"R. Kozlov","year":"2004","unstructured":"Kozlov R., Kvaerno A. and Owren B. (2004). The behaviour of the local error in splitting methods applied to stiff problems. J. Comput. Phys. 195: 576\u2013593","journal-title":"J. Comput. Phys."},{"issue":"6","key":"72_CR13","doi-asserted-by":"publisher","first-page":"715","DOI":"10.1007\/s00041-005-5017-6","volume":"11","author":"J. Lawrence","year":"2005","unstructured":"Lawrence J., Pfander G.E. and Walnut D. (2005). Linear independence of Gabor systems in finite dimensional vector spaces. J. Fourier Anal. Appl. 11(6): 715\u2013726","journal-title":"J. Fourier Anal. Appl."},{"key":"72_CR14","doi-asserted-by":"publisher","first-page":"410","DOI":"10.1016\/0022-1236(72)90037-7","volume":"10","author":"A. Lenard","year":"1972","unstructured":"Lenard A. (1972). The numerical range of projections. J. Funct. Anal. 10: 410\u2013413","journal-title":"J. Funct. Anal."},{"key":"72_CR15","unstructured":"Mathworks, Matlab, www.mathworks.com\/products\/matlab"},{"key":"72_CR16","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1016\/S0024-3795(02)00502-5","volume":"366","author":"M.K. Ng","year":"2003","unstructured":"Ng M.K., Bai Z.-Z. and Michael  (2003). A hybrid preconditioner of banded matrix approximation and alternating direction implicit iteration for symmetric sinc-Galerkin linear systems. Linear Algebra Appl. 366: 317\u2013335","journal-title":"Linear Algebra Appl."},{"key":"72_CR17","doi-asserted-by":"publisher","first-page":"506","DOI":"10.1137\/0705041","volume":"5","author":"G. Strang","year":"1968","unstructured":"Strang G. (1968). On the construction and comparison of difference schemes. SIAM J. Numer. Anal. 5: 506\u2013517","journal-title":"SIAM J. Numer. Anal."},{"key":"72_CR18","doi-asserted-by":"publisher","first-page":"840","DOI":"10.1137\/S0895479800377551","volume":"23","author":"A. Zanna","year":"2001","unstructured":"Zanna A. and Munthe-Kaas H. (2001). Generalized polar decompositions for the approximation of the matrix exponential. SIAM J. Matrix Anal. Appl. 23: 840\u2013862","journal-title":"SIAM J. Matrix Anal. Appl."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-007-0072-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00211-007-0072-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-007-0072-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-007-0072-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,18]],"date-time":"2022-05-18T04:08:07Z","timestamp":1652846887000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00211-007-0072-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,3,31]]},"references-count":18,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2007,5]]}},"alternative-id":["72"],"URL":"https:\/\/doi.org\/10.1007\/s00211-007-0072-3","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,3,31]]},"assertion":[{"value":"18 September 2006","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 February 2007","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 March 2007","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}