{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,10]],"date-time":"2024-09-10T02:45:11Z","timestamp":1725936311429},"publisher-location":"Cham","reference-count":23,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319724522"},{"type":"electronic","value":"9783319724539"}],"license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017]]},"DOI":"10.1007\/978-3-319-72453-9_6","type":"book-chapter","created":{"date-parts":[[2017,12,20]],"date-time":"2017-12-20T09:35:54Z","timestamp":1513762554000},"page":"81-94","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Efficient Certification of Numeric Solutions to\u00a0Eigenproblems"],"prefix":"10.1007","author":[{"given":"Joris","family":"van der Hoeven","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bernard","family":"Mourrain","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,12,21]]},"reference":[{"key":"6_CR1","volume-title":"Introduction to Interval Analysis","author":"G Alefeld","year":"1983","unstructured":"Alefeld, G., Herzberger, J.: Introduction to Interval Analysis. Academic Press, New York (1983)"},{"key":"6_CR2","unstructured":"Armentano, D., Beltr\u00e1n, C., B\u00fcrgisser, P., Cucker, F., Shub, M.: A stable, polynomial-time algorithm for the eigenpair problem. Technical report, arXiv (2014). \nhttp:\/\/arxiv.org\/abs\/1505.03290"},{"key":"6_CR3","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0701-6","volume-title":"Complexity and Real Computation","author":"L Blum","year":"1998","unstructured":"Blum, L., Cucker, F., Shub, M., Smale, S.: Complexity and Real Computation. Springer, New York (1998). \nhttps:\/\/doi.org\/10.1007\/978-1-4612-0701-6"},{"issue":"1","key":"6_CR4","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1137\/0720002","volume":"20","author":"JJ Dongarra","year":"1983","unstructured":"Dongarra, J.J., Moler, C.B., Wilkinson, J.H.: Improving the accuracy of computed eigenvalues and eigenvectors. SIAM J. Numer. Anal. 20(1), 23\u201345 (1983)","journal-title":"SIAM J. Numer. Anal."},{"key":"6_CR5","doi-asserted-by":"crossref","unstructured":"Le Gall, F.: Powers of tensors and fast matrix multiplication. In: Proceedings of ISSAC 2014, Kobe, Japan, pp. 296\u2013303, 23\u201325 July 2014","DOI":"10.1145\/2608628.2608664"},{"key":"6_CR6","volume-title":"Matrix Computations","author":"GH Golub","year":"1996","unstructured":"Golub, G.H., Van Loan, F.: Matrix Computations. JHU Press, Baltimore (1996)"},{"key":"6_CR7","doi-asserted-by":"crossref","unstructured":"Graillat, S., Tr\u00e9buchet, P.: A new algorithm for computing certified numerical approximations of the roots of a zero-dimensional system. In: Proceedings of ISSAC 2009, pp. 167\u2013174. ACM Press (2009)","DOI":"10.1145\/1576702.1576727"},{"key":"6_CR8","unstructured":"Harvey, D.: Faster truncated integer multiplication (2017). \nhttps:\/\/arxiv.org\/abs\/1703.00640"},{"key":"6_CR9","unstructured":"Harvey, D., van der Hoeven, J.: On the complexity of integer matrix multiplication. Technical report, HAL (2014, accepted for publication in JSC). \nhttp:\/\/hal.archives-ouvertes.fr\/hal-01071191"},{"key":"6_CR10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jco.2016.03.001","volume":"36","author":"D Harvey","year":"2016","unstructured":"Harvey, D., van der Hoeven, J., Lecerf, G.: Even faster integer multiplication. J. Complex. 36, 1\u201330 (2016)","journal-title":"J. Complex."},{"key":"6_CR11","unstructured":"van der Hoeven, J.: Ball arithmetic. Technical report, HAL (2009). \nhttp:\/\/hal.archives-ouvertes.fr\/hal-00432152"},{"key":"6_CR12","unstructured":"van der Hoeven, J., Lecerf, G., Mourrain, B., et al.: Mathemagix (2002). \nhttp:\/\/www.mathemagix.org"},{"key":"6_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-0249-6","volume-title":"Applied Interval Analysis","author":"L Jaulin","year":"2001","unstructured":"Jaulin, L., Kieffer, M., Didrit, O., Walter, E.: Applied Interval Analysis. Springer, London (2001). \nhttps:\/\/doi.org\/10.1007\/978-1-4471-0249-6"},{"issue":"3\/4","key":"6_CR14","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1145\/2576802.2576828","volume":"47","author":"F Johansson","year":"2014","unstructured":"Johansson, F.: Arb: a C library for ball arithmetic. ACM Commun. Comput. Algebra 47(3\/4), 166\u2013169 (2014)","journal-title":"ACM Commun. Comput. Algebra"},{"key":"6_CR15","series-title":"Studies in Mathematics","doi-asserted-by":"crossref","DOI":"10.1515\/9783110203196","volume-title":"Computer Arithmetic and Validity: Theory, Implementation, and Applications","author":"UW Kulisch","year":"2008","unstructured":"Kulisch, U.W.: Computer Arithmetic and Validity: Theory, Implementation, and Applications. Studies in Mathematics, vol. 33. de Gruyter, Berlin (2008)"},{"issue":"11","key":"6_CR16","doi-asserted-by":"crossref","first-page":"2994","DOI":"10.1016\/j.cam.2009.11.048","volume":"233","author":"S Miyajima","year":"2010","unstructured":"Miyajima, S.: Fast enclosure for all eigenvalues in generalized eigenvalue problems. J. Comput. Appl. Math. 233(11), 2994\u20133004 (2010)","journal-title":"J. Comput. Appl. Math."},{"key":"6_CR17","volume-title":"Interval Analysis","author":"RE Moore","year":"1966","unstructured":"Moore, R.E.: Interval Analysis. Prentice Hall, Englewood Cliffs (1966)"},{"key":"6_CR18","volume-title":"Interval Methods for Systems of Equations","author":"A Neumaier","year":"1990","unstructured":"Neumaier, A.: Interval Methods for Systems of Equations. Cambridge University Press, Cambridge (1990)"},{"key":"6_CR19","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1007\/s11075-009-9339-3","volume":"54","author":"S Rump","year":"2010","unstructured":"Rump, S., Graillat, S.: Verified error bounds for multiple roots of systems of nonlinear equations. Numer. Algorithms 54, 359\u2013377 (2010)","journal-title":"Numer. Algorithms"},{"issue":"2","key":"6_CR20","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/BF02239750","volume":"42","author":"SM Rump","year":"1989","unstructured":"Rump, S.M.: Guaranteed inclusions for the complex generalized eigenproblem. Computing 42(2), 225\u2013238 (1989)","journal-title":"Computing"},{"key":"6_CR21","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/978-94-017-1247-7_7","volume-title":"Developments in Reliable Computing","author":"SM Rump","year":"1999","unstructured":"Rump, S.M.: INTLAB - INTerval LABoratory. In: Csendes, T. (ed.) Developments in Reliable Computing, pp. 77\u2013104. Kluwer Academic Publishers, Dordrecht (1999). \nhttp:\/\/www.ti3.tu-harburg.de\/rump\/"},{"issue":"1\u20133","key":"6_CR22","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/S0024-3795(00)00279-2","volume":"324","author":"SM Rump","year":"2001","unstructured":"Rump, S.M.: Computational error bounds for multiple or nearly multiple eigenvalues. Linear Algebra Appl. 324(1\u20133), 209\u2013226 (2001)","journal-title":"Linear Algebra Appl."},{"issue":"2","key":"6_CR23","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/BF01396059","volume":"34","author":"T Yamamoto","year":"1980","unstructured":"Yamamoto, T.: Error bounds for computed eigenvalues and eigenvectors. Numerische Mathematik 34(2), 189\u2013199 (1980)","journal-title":"Numerische Mathematik"}],"container-title":["Lecture Notes in Computer Science","Mathematical Aspects of Computer and Information Sciences"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-72453-9_6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,12,20]],"date-time":"2017-12-20T09:37:28Z","timestamp":1513762648000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-72453-9_6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783319724522","9783319724539"],"references-count":23,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-72453-9_6","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2017]]}}}