{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T00:00:17Z","timestamp":1725494417948},"publisher-location":"Berlin, Heidelberg","reference-count":24,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540648482"},{"type":"electronic","value":"9783540685302"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1998]]},"DOI":"10.1007\/3-540-68530-8_10","type":"book-chapter","created":{"date-parts":[[2007,11,8]],"date-time":"2007-11-08T22:14:16Z","timestamp":1194560056000},"page":"115-126","source":"Crossref","is-referenced-by-count":3,"title":["Complexity Estimates Depending on Condition and Round-Off Error"],"prefix":"10.1007","author":[{"given":"Felipe","family":"Cucker","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Steve","family":"Smale","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2002,3,15]]},"reference":[{"key":"10_CR1","doi-asserted-by":"crossref","unstructured":"E.L. Allgower and K. Georg. Numerical Continuation Methods. Springer-Verlag, 1990.","DOI":"10.1007\/978-3-642-61257-2"},{"key":"10_CR2","doi-asserted-by":"crossref","unstructured":"J.L. Balc\u00e1zar, J. D\u00edaz, and J. Gabarr\u00f3. Structural Complexity I. EATCS Monographs on Theoretical Computer Science, 11. Springer-Verlag, 1988.","DOI":"10.1007\/978-3-642-97062-7"},{"key":"10_CR3","doi-asserted-by":"crossref","unstructured":"S. Basu, R. Pollack, and M.-F. Roy. On the combinatorial and algebraic complexity of quantifier elimination. In 35th annual IEEE Symp. on Foundations of Computer Science, pages 632\u2013641, 1994.","DOI":"10.1109\/SFCS.1994.365728"},{"key":"10_CR4","doi-asserted-by":"crossref","unstructured":"L. Blum, F. Cucker, M. Shub, and S. Smale. Complexity and Real Computation. Springer-Verlag, 1998.","DOI":"10.1007\/978-1-4612-0701-6"},{"key":"10_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1090\/S0273-0979-1989-15750-9","volume":"21","author":"L. Blum","year":"1989","unstructured":"L. Blum, M. Shub, and S. Smale. On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines. Bulletin of the Amer. Math. Soc., 21:1\u201346, 1989.","journal-title":"Bulletin of the Amer. Math. Soc."},{"key":"10_CR6","unstructured":"S.L. Campbell and C.D. Meyer. Generalized Inverses of Linear Transformations. Pitman, 1979."},{"key":"10_CR7","doi-asserted-by":"crossref","unstructured":"G.E. Collins. Quantifier elimination for real closed fields by cylindrical algebraic deccomposition, volume 33 of Lect. Notes in Comp. Sci., pages 134\u2013183. Springer-Verlag, 1975.","DOI":"10.1007\/3-540-07407-4_17"},{"key":"10_CR8","doi-asserted-by":"crossref","unstructured":"F. Cucker and S. Smale. Complexity estimates depending on condition and round-off error. Preprint, 1997.","DOI":"10.1007\/3-540-68530-8_10"},{"key":"10_CR9","unstructured":"J.-P. Dedieu and M. Shub. Multihomogeneous Newton methods. Preprint, 1997."},{"key":"10_CR10","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/S0747-7171(88)80005-1","volume":"5","author":"D.Yu. Grigoriev","year":"1988","unstructured":"D.Yu. Grigoriev and N.N. Vorobjov. Solving systems of polynomial inequalities in subexponential time. Journal of Symbolic Computation, 5:37\u201364, 1988.","journal-title":"Journal of Symbolic Computation"},{"key":"10_CR11","doi-asserted-by":"crossref","first-page":"101","DOI":"10.24033\/bsmf.2138","volume":"118","author":"J. Heintz","year":"1990","unstructured":"J. Heintz, M.-F. Roy, and P. Solerno. Sur la complexit\u00e9 du principe de Tarski-Seidenberg. Bulletin de la Soci\u00e9t\u00e9 Math\u00e9matique de France, 118:101\u2013126, 1990.","journal-title":"Bulletin de la Soci\u00e9t\u00e9 Math\u00e9matique de France"},{"key":"10_CR12","unstructured":"N. Higham. Accuracy and Stability of Numerical Algorithms. SIAM, 1996."},{"key":"10_CR13","unstructured":"C.H. Papadimitriou. Computational Complexity. Addison-Wesley, 1994."},{"key":"10_CR14","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1016\/S0747-7171(10)80003-3","volume":"13","author":"J. Renegar","year":"1992","unstructured":"J. Renegar. On the computational complexity and geometry of the first-order theory of the reals. Part I. Journal of Symbolic Computation, 13:255\u2013299, 1992.","journal-title":"Journal of Symbolic Computation"},{"key":"10_CR15","doi-asserted-by":"publisher","first-page":"459","DOI":"10.2307\/2152805","volume":"6","author":"M. Shub","year":"1993","unstructured":"M. Shub and S. Smale. Complexity of Bezout\u2019s theorem I: geometric aspects. Journal of the Amer. Math. Soc., 6:459\u2013501, 1993.","journal-title":"Journal of the Amer. Math. Soc."},{"key":"10_CR16","doi-asserted-by":"crossref","unstructured":"M. Shub and S. Smale. Complexity of Bezout\u2019s theorem II: volumes and probabilities. In F. Eyssette and A. Galligo, editors, Computational Algebraic Geometry, volume 109 of Progress in Mathematics, pages 267\u2013285. Birkh\u00e4user, 1993.","DOI":"10.1007\/978-1-4612-2752-6_19"},{"key":"10_CR17","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1006\/jcom.1993.1002","volume":"9","author":"M. Shub","year":"1993","unstructured":"M. Shub and S. Smale. Complexity of Bezout\u2019s theorem III: condition number and packing. Journal of Complexity, 9:4\u201314, 1993.","journal-title":"Journal of Complexity"},{"key":"10_CR18","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1016\/0304-3975(94)90122-8","volume":"133","author":"M. Shub","year":"1994","unstructured":"M. Shub and S. Smale. Complexity of Bezout\u2019s theorem V: polynomial time. Theoretical Computer Science, 133:141\u2013164, 1994.","journal-title":"Theoretical Computer Science"},{"key":"10_CR19","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1137\/0733008","volume":"33","author":"M. Shub","year":"1996","unstructured":"M. Shub and S. Smale. Complexity of Bezout\u2019s theorem IV: probability of success; extensions. SIAM J. of Numer. Anal., 33:128\u2013148, 1996.","journal-title":"SIAM J. of Numer. Anal."},{"key":"10_CR20","doi-asserted-by":"crossref","unstructured":"S. Smale. Complexity theory and numerical analysis. In A. Iserles, editor, Acta Numerica, pages 523\u2013551. Cambridge University Press, 1997.","DOI":"10.1017\/S0962492900002774"},{"key":"10_CR21","doi-asserted-by":"crossref","unstructured":"A. Tarski. A Decision Method for Elementary Algebra and Geometry. University of California Press, 1951.","DOI":"10.1525\/9780520348097"},{"key":"10_CR22","doi-asserted-by":"crossref","unstructured":"L.N. Trefethen and D. Bau III. Numerical Linear Algebra. SIAM, 1997.","DOI":"10.1137\/1.9780898719574"},{"key":"10_CR23","unstructured":"J. Wilkinson. Rounding Errors in Algebraic Processes. Prentice Hall, 1963."},{"key":"10_CR24","doi-asserted-by":"publisher","first-page":"548","DOI":"10.1137\/1013095","volume":"13","author":"J. Wilkinson","year":"1971","unstructured":"J. Wilkinson. Modern error analyis. SIAM Review, 13:548\u2013568, 1971.","journal-title":"SIAM Review"}],"container-title":["Lecture Notes in Computer Science","Algorithms \u2014 ESA\u2019 98"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-68530-8_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,14]],"date-time":"2023-05-14T17:24:25Z","timestamp":1684085065000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-68530-8_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998]]},"ISBN":["9783540648482","9783540685302"],"references-count":24,"URL":"https:\/\/doi.org\/10.1007\/3-540-68530-8_10","relation":{},"ISSN":["0302-9743"],"issn-type":[{"type":"print","value":"0302-9743"}],"subject":[],"published":{"date-parts":[[1998]]}}}