乐胖代购免代理版

{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T00:12:31Z","timestamp":1726013551583},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2021,10,26]],"date-time":"2021-10-26T00:00:00Z","timestamp":1635206400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,10,26]],"date-time":"2021-10-26T00:00:00Z","timestamp":1635206400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["TRR 146"],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["TRR 154"],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["SPP 2256"],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100008131","name":"Rheinische Friedrich-Wilhelms-Universit\u00e4t Bonn","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100008131","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2021,12]]},"abstract":"Abstract<\/jats:title>The numerical solution of dynamical systems with memory requires the efficient evaluation of Volterra integral operators in an evolutionary manner. After appropriate discretization, the basic problem can be represented as a matrix-vector product with a lower diagonal but densely populated matrix. For typical applications, like fractional diffusion or large-scale dynamical systems with delay, the memory cost for storing the matrix approximations and complete history of the data then becomes prohibitive for an accurate numerical approximation. For Volterra integral operators of convolution type, thefast and oblivious convolution quadrature<\/jats:italic>method of Sch\u00e4dle, Lopez-Fernandez, and Lubich resolves this issue and allows to compute the discretized evaluation withN<\/jats:italic>time steps in

$O(N \\log N)$<\/jats:tex-math>O<\/mml:mi>(<\/mml:mo>N<\/mml:mi>log<\/mml:mi>N<\/mml:mi>)<\/mml:mo><\/mml:math><\/jats:alternatives><\/jats:inline-formula>complexity and only requires

${{\\mathscr{H}}}$<\/jats:tex-math>H<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>-matrix approximation of the underlying integral operator. A further improvement can thus be achieved, in principle, by resorting to

${{\\mathscr{H}}}^{2}$<\/jats:tex-math>H<\/mml:mi><\/mml:mrow>2<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:math><\/jats:alternatives><\/jats:inline-formula>-matrix-vector product for discretized Volterra integral operators that can be performed in an evolutionary and oblivious manner and requires onlyO<\/jats:italic>(N<\/jats:italic>) operations and

$O(\\log N)$<\/jats:tex-math>O<\/mml:mi>(<\/mml:mo>log<\/mml:mi>N<\/mml:mi>)<\/mml:mo><\/mml:math><\/jats:alternatives><\/jats:inline-formula>active memory. In addition to the acceleration, more general asymptotically smooth kernels can be treated and the algorithm does not require a priori knowledge of the number of time steps. The efficiency of the proposed method is demonstrated by application to some typical test problems.<\/jats:p>","DOI":"10.1007\/s10444-021-09902-6","type":"journal-article","created":{"date-parts":[[2021,10,26]],"date-time":"2021-10-26T03:37:58Z","timestamp":1635219478000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A fast and oblivious matrix compression algorithm for Volterra integral operators"],"prefix":"10.1007","volume":"47","author":[{"ORCID":"http:\/\/orcid.org\/0000-0003-3322-1187","authenticated-orcid":false,"given":"J.","family":"D\u00f6lz","sequence":"first","affiliation":[]},{"given":"H.","family":"Egger","sequence":"additional","affiliation":[]},{"given":"V.","family":"Shashkov","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,10,26]]},"reference":[{"issue":"4","key":"9902_CR1","doi-asserted-by":"publisher","first-page":"1138","DOI":"10.1137\/S0036142998336916","volume":"37","author":"B Alpert","year":"2000","unstructured":"Alpert, B., Greengard, L., Hagstrom, T.: Rapid evaluation of nonreflecting boundary kernels for time-domain wave propagation. SIAM J. Numer. Anal. 37(4), 1138\u20131164 (2000)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"9902_CR2","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1007\/BF00337259","volume":"27","author":"S Amari","year":"1977","unstructured":"Amari, S.: Dynamics of pattern formation in lateral-inhibition type neural fields. Biol. Cybern. 27(2), 77\u201387 (1977)","journal-title":"Biol. Cybern."},{"key":"9902_CR3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-0087-7","volume-title":"Vector-Valued Laplace Transforms and Cauchy Problems","author":"W Arendt","year":"2011","unstructured":"Arendt, W., Batty, C.J.K., Hieber, M., Neubrander, F.: Vector-Valued Laplace Transforms and Cauchy Problems. Springer Basel, Basel (2011)"},{"issue":"2","key":"9902_CR4","doi-asserted-by":"publisher","first-page":"496","DOI":"10.1137\/15M1043960","volume":"55","author":"D Baffet","year":"2017","unstructured":"Baffet, D., Hesthaven, J.S.: A kernel compression scheme for fractional differential equations. SIAM J. Numer. Anal. 55(2), 496\u2013520 (2017)","journal-title":"SIAM J. Numer. Anal."},{"key":"9902_CR5","doi-asserted-by":"crossref","unstructured":"B\u00f6rm, S.: Efficient Numerical Methods for Non-Local Operators, volume 14 of EMS Tracts in Mathematics, European Mathematical Society (EMS) Z\u00fcrich (2010)","DOI":"10.4171\/091"},{"issue":"2","key":"9902_CR6","doi-asserted-by":"publisher","first-page":"348","DOI":"10.1016\/0021-9991(90)90171-V","volume":"90","author":"A Brandt","year":"1990","unstructured":"Brandt, A., Lubrecht, A.A.: Multilevel matrix multiplication and fast solution of integral equations. J. Comput. Phys. 90(2), 348\u2013370 (1990)","journal-title":"J. Comput. Phys."},{"key":"9902_CR7","volume-title":"Collocation Methods for Volterra Integral and Related Functional Differential Equations. Number 15 in Cambridge Monographs on Applied and Computational Mathematics","author":"H Brunner","year":"2004","unstructured":"Brunner, H.: Collocation Methods for Volterra Integral and Related Functional Differential Equations. Number 15 in Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, Cambridge (2004)"},{"key":"9902_CR8","doi-asserted-by":"publisher","DOI":"10.1017\/9781316162491","volume-title":"Volterra Integral Equations: An Introduction to Theory and Applications","author":"H Brunner","year":"2017","unstructured":"Brunner, H.: Volterra Integral Equations: An Introduction to Theory and Applications. Cambridge University Press, Cambridge (2017)"},{"issue":"254","key":"9902_CR9","doi-asserted-by":"publisher","first-page":"673","DOI":"10.1090\/S0025-5718-06-01788-1","volume":"75","author":"E Cuesta","year":"2006","unstructured":"Cuesta, E., Lubich, C., Palencia, C.: Convolution quadrature time discretization of fractional diffusion-wave equations. Math. Comput. 75 (254), 673\u2013697 (2006)","journal-title":"Math. Comput."},{"issue":"3","key":"9902_CR10","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1007\/BF02072014","volume":"1","author":"W Dahmen","year":"1993","unstructured":"Dahmen, W., Pr\u00f6ssdorf, S., Schneider, R.: Wavelet approximation methods for pseudodifferential equations II: matrix compression and fast solution. Adv. Comput. Math. 1(3), 259\u2013335 (1993)","journal-title":"Adv. Comput. Math."},{"issue":"1","key":"9902_CR11","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1007\/s11075-014-9895-z","volume":"68","author":"B Dingfelder","year":"2015","unstructured":"Dingfelder, B., Weideman, J.A.C.: An improved Talbot method for numerical Laplace transform inversion. Numer. Algorithm. 68(1), 167\u2013183 (2015)","journal-title":"Numer. Algorithm."},{"key":"9902_CR12","doi-asserted-by":"crossref","unstructured":"D\u00f6lz, J., Egger, H., Shashkov, V: A convolution quadrature method for Maxwell\u2019s equations in dispersive media (2020)","DOI":"10.1007\/978-3-030-84238-3_11"},{"key":"9902_CR13","doi-asserted-by":"publisher","first-page":"112618","DOI":"10.1016\/j.cam.2019.112618","volume":"387","author":"H Egger","year":"2020","unstructured":"Egger, H., Schmidt, K., Shashkov, V.: Multistep and Runge-Kutta convolution quadrature methods for coupled dynamical systems. J. Comput. Appl. Math. 387, 112618 (2020)","journal-title":"J. Comput. Appl. Math."},{"issue":"23","key":"9902_CR14","doi-asserted-by":"publisher","first-page":"8712","DOI":"10.1016\/j.jcp.2009.08.031","volume":"228","author":"W Fong","year":"2009","unstructured":"Fong, W., Darve, E.: The black-box fast multipole method. J. Comput. Phys. 228(23), 8712\u20138725 (2009)","journal-title":"J. Comput. Phys."},{"issue":"3","key":"9902_CR15","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1007\/s006070170005","volume":"67","author":"K Giebermann","year":"2001","unstructured":"Giebermann, K.: Multilevel approximation of boundary integral operators. Computing 67(3), 183\u2013207 (2001)","journal-title":"Computing"},{"issue":"2","key":"9902_CR16","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1016\/0021-9991(87)90140-9","volume":"73","author":"L Greengard","year":"1987","unstructured":"Greengard, L., Rokhlin, V.: A fast algorithm for particle simulations. J. Comput. Phys. 73(2), 325\u2013348 (1987)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"9902_CR17","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1007\/s006070050015","volume":"62","author":"W Hackbusch","year":"1999","unstructured":"Hackbusch, W.: A sparse matrix arithmetic based on ${\\mathscr{H}}$-matrices part I: introduction to ${\\mathscr{H}}$-matrices. Computing 62(2), 89\u2013108 (1999)","journal-title":"Computing"},{"key":"9902_CR18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-47324-5","volume-title":"Hierarchical Matrices: Algorithms and Analysis","author":"W Hackbusch","year":"2015","unstructured":"Hackbusch, W.: Hierarchical Matrices: Algorithms and Analysis. Springer, Heidelberg (2015)"},{"issue":"4","key":"9902_CR19","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1007\/BF01396324","volume":"54","author":"W Hackbusch","year":"1989","unstructured":"Hackbusch, W., Nowak, Z.P.: On the fast matrix multiplication in the boundary element method by panel clustering. Numer. Math. 54(4), 463\u2013491 (1989)","journal-title":"Numer. Math."},{"key":"9902_CR20","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1017\/S0962492900002890","volume":"8","author":"T Hagstrom","year":"1999","unstructured":"Hagstrom, T.: Radiation boundary conditions for the numerical simulation of waves. Acta Numerica 8, 47\u2013106 (1999)","journal-title":"Acta Numerica"},{"issue":"3","key":"9902_CR21","doi-asserted-by":"publisher","first-page":"532","DOI":"10.1137\/0906037","volume":"6","author":"E Hairer","year":"1985","unstructured":"Hairer, E., Lubich, C. h., Schlichte, M.: Fast numerical solution of nonlinear Volterra convolution equations. SIAM J. Sci. Stat. Comput. 6(3), 532\u2013541 (1985)","journal-title":"SIAM J. Sci. Stat. Comput."},{"issue":"6-7","key":"9902_CR22","doi-asserted-by":"publisher","first-page":"955","DOI":"10.1016\/S0898-1221(04)90079-X","volume":"47","author":"S Jiang","year":"2004","unstructured":"Jiang, S., Greengard, L.: Fast evaluation of nonreflecting boundary conditions for the Schr\u00f6dinger equation in one dimension. Comput. Math. Appl. 47(6-7), 955\u2013966 (2004)","journal-title":"Comput. Math. Appl."},{"issue":"2","key":"9902_CR23","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1002\/cpa.20200","volume":"61","author":"S Jiang","year":"2008","unstructured":"Jiang, S., Greengard, L.: Efficient representation of nonreflecting boundary conditions for the time-dependent Schr\u00f6dinger equation in two dimensions. Commun. Pure Appl. Math. 61(2), 261\u2013288 (2008)","journal-title":"Commun. Pure Appl. Math."},{"key":"9902_CR24","doi-asserted-by":"crossref","unstructured":"Kapur, S., Long, D.E., Roychowdhury, J.: Efficient time-domain simulation of frequency-dependent elements. In: Proceedings of International Conference on Computer Aided Design, pp 569\u2013573. IEEE Comput. Soc. Press, San Jose, CA, USA (1996)","DOI":"10.1109\/ICCAD.1996.569912"},{"issue":"4","key":"9902_CR25","doi-asserted-by":"publisher","first-page":"091","DOI":"10.21468\/SciPostPhys.10.4.091","volume":"10","author":"J Kaye","year":"2021","unstructured":"Kaye, J., Gole\u017e, D.: Low rank compression in the numerical solution of the nonequilibrium Dyson equation. SciPost Phys. 10(4), 091 (2021)","journal-title":"SciPost Phys."},{"issue":"3","key":"9902_CR26","doi-asserted-by":"publisher","first-page":"1332","DOI":"10.1137\/050629653","volume":"44","author":"M L\u00f3pez-Fern\u00e1ndez","year":"2006","unstructured":"L\u00f3pez-Fern\u00e1ndez, M., Palencia, C., Sch\u00e4dle, A.: A spectral order method for inverting sectorial laplace transforms. SIAM J. Numer. Anal. 44(3), 1332\u20131350 (2006)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"9902_CR27","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/BF01398686","volume":"52","author":"CH Lubich","year":"1988","unstructured":"Lubich, C.H.: Convolution quadrature and discretized operational calculus. I. Numer. Math. 52(2), 129\u2013145 (1988)","journal-title":"I. Numer. Math."},{"issue":"4","key":"9902_CR28","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1007\/BF01462237","volume":"52","author":"CH Lubich","year":"1988","unstructured":"Lubich, C.H.: Convolution quadrature discretized operational calculus. II. Numer. Math. 52(4), 413\u2013425 (1988)","journal-title":"II. Numer. Math."},{"issue":"3","key":"9902_CR29","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1023\/B:BITN.0000046813.23911.2d","volume":"44","author":"CH Lubich","year":"2004","unstructured":"Lubich, C.H.: Convolution quadrature revisited. BIT Numer. Math. 44(3), 503\u2013514 (2004)","journal-title":"BIT Numer. Math."},{"issue":"201","key":"9902_CR30","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1090\/S0025-5718-1993-1153166-7","volume":"60","author":"CH Lubich","year":"1993","unstructured":"Lubich, C.H., Ostermann, A.: Runge-Kutta methods for parabolic equations and convolution quadrature. Math. Comput. 60(201), 105\u2013105 (1993)","journal-title":"Math. Comput."},{"issue":"1","key":"9902_CR31","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1137\/S1064827501388741","volume":"24","author":"CH Lubich","year":"2002","unstructured":"Lubich, C.H., Sch\u00e4dle, A.: Fast convolution for nonreflecting boundary conditions. SIAM J. Sci. Comput. 24(1), 161\u2013182 (2002)","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"9902_CR32","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0370-1573(00)00070-3","volume":"339","author":"R Metzler","year":"2000","unstructured":"Metzler, R., Klafter, J.: The random walk\u2019s guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep. 339(1), 1\u201377 (2000)","journal-title":"Phys. Rep."},{"issue":"2","key":"9902_CR33","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1016\/0021-9991(85)90002-6","volume":"60","author":"V Rokhlin","year":"1985","unstructured":"Rokhlin, V.: Rapid solution of integral equations of classical potential theory. J. Comput. Phys. 60(2), 187\u2013207 (1985)","journal-title":"J. Comput. Phys."},{"key":"9902_CR34","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-26645-9","volume-title":"Retarded Potentials and Time Domain Boundary Integral Equations, volume 50 of Springer Series in Computational Mathematics","author":"F-J Sayas","year":"2016","unstructured":"Sayas, F.-J.: Retarded Potentials and Time Domain Boundary Integral Equations, volume 50 of Springer Series in Computational Mathematics. Springer International Publishing, Cham (2016)"},{"issue":"2","key":"9902_CR35","doi-asserted-by":"publisher","first-page":"421","DOI":"10.1137\/050623139","volume":"28","author":"A Sch\u00e4dle","year":"2006","unstructured":"Sch\u00e4dle, A., L\u00f3pez-Fern\u00e1ndez, M., Lubich, C.H.: Fast and oblivious convolution quadrature. SIAM J. Sci. Comput. 28(2), 421\u2013438 (2006)","journal-title":"SIAM J. Sci. Comput."},{"issue":"3","key":"9902_CR36","doi-asserted-by":"publisher","first-page":"267","DOI":"10.21136\/CPM.1979.118022","volume":"104","author":"M Sova","year":"1979","unstructured":"Sova, M.: The Laplace transform of analytic vector-valued functions (complex conditions). \u010cas. pro p\u011bstov\u00e1n\u00ed matematiky 104(3), 267\u2013280 (1979)","journal-title":"\u010cas. pro p\u011bstov\u00e1n\u00ed matematiky"},{"issue":"1","key":"9902_CR37","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1093\/imamat\/23.1.97","volume":"23","author":"A Talbot","year":"1979","unstructured":"Talbot, A.: The accurate numerical inversion of laplace transforms. IMA J. Appl. Math. 23(1), 97\u2013120 (1979)","journal-title":"IMA J. Appl. Math."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-021-09902-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10444-021-09902-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-021-09902-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,10]],"date-time":"2024-09-10T20:18:33Z","timestamp":1725999513000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10444-021-09902-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,26]]},"references-count":37,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["9902"],"URL":"https:\/\/doi.org\/10.1007\/s10444-021-09902-6","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"type":"print","value":"1019-7168"},{"type":"electronic","value":"1572-9044"}],"subject":[],"published":{"date-parts":[[2021,10,26]]},"assertion":[{"value":"24 March 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 September 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 October 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"81"}}