{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T08:32:46Z","timestamp":1725870766606},"publisher-location":"Cham","reference-count":27,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319399270"},{"type":"electronic","value":"9783319399294"}],"license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016]]},"DOI":"10.1007\/978-3-319-39929-4_24","type":"book-chapter","created":{"date-parts":[[2016,11,10]],"date-time":"2016-11-10T07:11:44Z","timestamp":1478761904000},"page":"237-253","source":"Crossref","is-referenced-by-count":1,"title":["Multigrid at Scale?"],"prefix":"10.1007","author":[{"given":"Mark","family":"Ainsworth","sequence":"first","affiliation":[]},{"given":"Christian","family":"Glusa","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,11,11]]},"reference":[{"key":"24_CR1","unstructured":"M. Ainsworth, C. Glusa, Is the multigrid method fault-tolerant? The Two Grid Case (Submitted)"},{"key":"24_CR2","unstructured":"M. Ainsworth, C. Glusa, Is the multigrid method fault-tolerant? The Multi Grid Case (In preparation)"},{"issue":"1","key":"24_CR3","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1109\/TDSC.2004.2","volume":"1","author":"A. Avi\u017eienis","year":"2004","unstructured":"A.\u00a0Avi\u017eienis, J.-C. Laprie, B.\u00a0Randell, C.\u00a0Landwehr, Basic concepts and taxonomy of dependable and secure computing. IEEE Trans. Dependable Secure Comput. 1 (1), 11\u201333 (2004)","journal-title":"IEEE Trans. Dependable Secure Comput."},{"key":"24_CR4","doi-asserted-by":"crossref","unstructured":"P.\u00a0Bougerol, J.\u00a0Lacroix, Products of Random Matrices with Applications to Schr\u00f6dinger Operators. Progress in Probability and Statistics, vol.\u00a08 (Birkh\u00e4user Boston Inc., Boston, 1985)","DOI":"10.1007\/978-1-4684-9172-2"},{"key":"24_CR5","unstructured":"J.H. Bramble, Multigrid Methods, vol.\u00a0294 (Longman Scientific & Technical, Harlow, 1993)"},{"issue":"3","key":"24_CR6","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1177\/1094342009106189","volume":"23","author":"F. Cappello","year":"2009","unstructured":"F.\u00a0Cappello, Fault tolerance in petascale\/exascale systems: current knowledge, challenges and research opportunities. Int. J. High Perform. Comput. Appl. 23 (3), 212\u2013226 (2009)","journal-title":"Int. J. High Perform. Comput. Appl."},{"key":"24_CR7","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1177\/1094342009347767","volume":"23","author":"F. Cappello","year":"2009","unstructured":"F.\u00a0Cappello, A.\u00a0Geist, B.\u00a0Gropp, L.\u00a0Kale, B.\u00a0Kramer, M.\u00a0Snir, Toward exascale resilience. Int. J. High Perform. Comput. Appl. 23, 374\u2013388 (2009)","journal-title":"Int. J. High Perform. Comput. Appl."},{"issue":"1","key":"24_CR8","first-page":"5","volume":"1","author":"F. Cappello","year":"2014","unstructured":"F.\u00a0Cappello, A.\u00a0Geist, W.\u00a0Gropp, S.\u00a0Kale, B.\u00a0Kramer, M.\u00a0Snir, Toward exascale resilience: 2014 update. Supercomput. Front. Innov. 1 (1), 5\u201328 (2014)","journal-title":"Supercomput. Front. Innov."},{"key":"24_CR9","first-page":"91","volume-title":"Fault Resilience of the Algebraic Multi-grid Solver (ICS\u201912)","author":"M. Casas","year":"2012","unstructured":"M.\u00a0Casas, B.R. de\u00a0Supinski, G.\u00a0Bronevetsky, M.\u00a0Schulz, Fault Resilience of the Algebraic Multi-grid Solver (ICS\u201912) (ACM, New York, 2012), pp.\u00a091\u2013100"},{"key":"24_CR10","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-84942-8","volume-title":"Products of Random Matrices","author":"A. Crisanti","year":"1993","unstructured":"A.\u00a0Crisanti, G.\u00a0Paladin, A.\u00a0Vulpiani, Products of Random Matrices (Springer, Berlin\/Heidelberg, 1993)"},{"key":"24_CR11","unstructured":"T.\u00a0Cui, J.\u00a0Xu, C.-S. Zhang, An Error-Resilient Redundant Subspace Correction Method, ArXiv e-prints (2013)"},{"key":"24_CR12","doi-asserted-by":"crossref","DOI":"10.2172\/1089338","volume-title":"Quantifying the impact of single bit flips on floating point arithmetic, Technical report ORNL\/TM-2013\/282","author":"J. Elliott","year":"2013","unstructured":"J.\u00a0Elliott, F.\u00a0Mueller, M.\u00a0Stoyanov, C.G. Webster, Quantifying the impact of single bit flips on floating point arithmetic, Technical report ORNL\/TM-2013\/282, Oak Ridge National Laboratory, 2013"},{"key":"24_CR13","unstructured":"M.\u00a0Embree, L.N. Trefethen, Growth and decay of random Fibonacci sequences. Proc.: Math. Phys. Eng. Sci. 455 (1987), 2471\u20132485 (1999) (English)"},{"issue":"2","key":"24_CR14","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1214\/aoms\/1177705909","volume":"31","author":"H. Furstenberg","year":"1960","unstructured":"H.\u00a0Furstenberg, H.\u00a0Kesten, Products of random matrices. Ann. Math. Stat. 31 (2), 457\u2013469 (1960)","journal-title":"Ann. Math. Stat."},{"key":"24_CR15","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-02427-0","volume-title":"Multi-grid Methods and Applications","author":"W. Hackbusch","year":"1985","unstructured":"W.\u00a0Hackbusch, Multi-grid Methods and Applications, vol.\u00a04 (Springer, Berlin, 1985)"},{"key":"24_CR16","doi-asserted-by":"crossref","unstructured":"W.\u00a0Hackbusch, Iterative Solution of Large Sparse Systems of Equations. Applied Mathematical Sciences, vol.\u00a095 (Springer, New\u00a0York, 1994). Translated and revised from the 1991 German original","DOI":"10.1007\/978-1-4612-4288-8"},{"key":"24_CR17","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-20943-2","volume-title":"Fault-Tolerance Techniques for High-Performance Computing","author":"T. Herault","year":"2015","unstructured":"T.\u00a0Herault, Y.\u00a0Robert, Fault-Tolerance Techniques for High-Performance Computing (Springer, Cham, 2015)"},{"issue":"6","key":"24_CR18","doi-asserted-by":"crossref","first-page":"518","DOI":"10.1109\/TC.1984.1676475","volume":"100","author":"K.-H. Huang","year":"1984","unstructured":"K.-H. Huang, J.\u00a0Abraham, Algorithm-based fault tolerance for matrix operations. IEEE Trans. Comput. 100 (6), 518\u2013528 (1984)","journal-title":"IEEE Trans. Comput."},{"key":"24_CR19","unstructured":"M.\u00a0Huber, B.\u00a0Gmeiner, U.\u00a0R\u00fcde, B.\u00a0Wohlmuth, Resilience for multigrid software at the extreme scale, arXiv preprint arXiv:1506.06185 (2015)"},{"key":"24_CR20","doi-asserted-by":"crossref","first-page":"1965","DOI":"10.1103\/PhysRevLett.68.1965","volume":"68","author":"R. Mainieri","year":"1992","unstructured":"R.\u00a0Mainieri, Zeta function for the Lyapunov exponent of a product of random matrices. Phys. Rev. Lett. 68, 1965\u20131968 (1992)","journal-title":"Phys. Rev. Lett."},{"key":"24_CR21","volume-title":"A Multigrid Tutorial","author":"S.F. McCormick","year":"2000","unstructured":"S.F. McCormick, W.L. Briggs, V.E. Henson, A Multigrid Tutorial (SIAM, Philadelphia, 2000)"},{"key":"24_CR22","first-page":"152","volume-title":"Characterizing the Impact of Soft Errors on Iterative Methods in Scientific Computing (ICS\u201911)","author":"M. Shantharam","year":"2011","unstructured":"M.\u00a0Shantharam, S.\u00a0Srinivasmurthy, P.\u00a0Raghavan, Characterizing the Impact of Soft Errors on Iterative Methods in Scientific Computing (ICS\u201911) (ACM, New York, 2011), pp.\u00a0152\u2013161"},{"key":"24_CR23","doi-asserted-by":"crossref","unstructured":"J.\u00a0Sloan, R.\u00a0Kumar, G.\u00a0Bronevetsky, Algorithmic approaches to low overhead fault detection for sparse linear algebra, in 2012 42nd Annual IEEE\/IFIP International Conference on Dependable Systems and Networks (DSN), Boston (IEEE, 2012), pp.\u00a01\u201312","DOI":"10.1109\/DSN.2012.6263938"},{"issue":"2","key":"24_CR24","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1177\/1094342014522573","volume":"28","author":"M. Snir","year":"2014","unstructured":"M.\u00a0Snir, R.W. Wisniewski, J.A. Abraham, S.V. Adve, S.\u00a0Bagchi, P.\u00a0Balaji, J.\u00a0Belak, P.\u00a0Bose, F.\u00a0Cappello, B.\u00a0Carlson, et\u00a0al., Addressing failures in exascale computing. Int. J. High Perform. Comput. Appl. 28 (2), 129\u2013173 (2014)","journal-title":"Int. J. High Perform. Comput. Appl."},{"issue":"5","key":"24_CR25","doi-asserted-by":"crossref","first-page":"C532","DOI":"10.1137\/140991406","volume":"37","author":"M. Stoyanov","year":"2015","unstructured":"M.\u00a0Stoyanov, C.\u00a0Webster, Numerical analysis of fixed point algorithms in the presence of hardware faults. SIAM J. Sci. Comput. 37 (5), C532\u2013C553 (2015)","journal-title":"SIAM J. Sci. Comput."},{"key":"24_CR26","unstructured":"U.\u00a0Trottenberg, C.W. Oosterlee, A.\u00a0Sch\u00fcller, Multigrid (Academic Press Inc., San Diego, 2001). With contributions by A. Brandt, P.\u00a0Oswald and K. St\u00fcben"},{"issue":"1","key":"24_CR27","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/BF01219774","volume":"10","author":"J.N. Tsitsiklis","year":"1997","unstructured":"J.N. Tsitsiklis, V.D. Blondel, The Lyapunov exponent and joint spectral radius of pairs of matrices are hard-when not impossible-to compute and to approximate. Math. Control Signals Syst. 10 (1), 31\u201340 (1997) (English)","journal-title":"Math. Control Signals Syst."}],"container-title":["Lecture Notes in Computational Science and Engineering","Numerical Mathematics and Advanced Applications ENUMATH 2015"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-39929-4_24","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,15]],"date-time":"2019-09-15T08:51:07Z","timestamp":1568537467000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-39929-4_24"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"ISBN":["9783319399270","9783319399294"],"references-count":27,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-39929-4_24","relation":{},"ISSN":["1439-7358","2197-7100"],"issn-type":[{"type":"print","value":"1439-7358"},{"type":"electronic","value":"2197-7100"}],"subject":[],"published":{"date-parts":[[2016]]}}}