{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T16:39:47Z","timestamp":1759941587374},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[1994,9,1]],"date-time":"1994-09-01T00:00:00Z","timestamp":778377600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[1994,9]]},"DOI":"10.1007\/bf02140678","type":"journal-article","created":{"date-parts":[[2005,9,15]],"date-time":"2005-09-15T12:03:51Z","timestamp":1126785831000},"page":"129-143","source":"Crossref","is-referenced-by-count":21,"title":["The equality relations in scientific computing"],"prefix":"10.1007","volume":"7","author":[{"given":"Jean-Marie","family":"Chesneaux","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"BF02140678_CR1","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1016\/0378-4754(88)90072-9","volume":"30","author":"R. Alt","year":"1988","unstructured":"R. Alt, Floating point error propagation in iterative methods, Math. Comp. Simul. 30 (1988) 505\u2013517.","journal-title":"Math. Comp. Simul."},{"key":"BF02140678_CR2","first-page":"417","volume":"307","author":"J.-M. Chesneaux","year":"1988","unstructured":"J.-M. Chesneaux, Mod\u00e9lisation et conditions de validit\u00e9 de la m\u00e9thode CESTAC, C.R. Acad. Sci., Paris, s\u00e9r. 1, 307 (1988) 417\u2013422.","journal-title":"C.R. Acad. Sci., Paris, s\u00e9r. 1"},{"key":"BF02140678_CR3","volume-title":"Etude th\u00e9orique et impl\u00e9mentation en ADA de la m\u00e9thode CESTAC","author":"J.-M. Chesneaux","year":"1988","unstructured":"J.-M. Chesneaux, Etude th\u00e9orique et impl\u00e9mentation en ADA de la m\u00e9thode CESTAC, Thesis, Universit\u00e9 P. et M. Curie, Paris (1988)."},{"key":"BF02140678_CR4","first-page":"855","volume":"307","author":"J.-M. Chesneaux","year":"1988","unstructured":"J.-M. Chesneaux and J. Vignes, Sur la robustesse de la m\u00e9thode CESTAC, C.R. Acad. Sci., Paris, s\u00e9r. 1, 307 (1988) 855\u2013860.","journal-title":"C.R. Acad. Sci., Paris, s\u00e9r. 1"},{"key":"BF02140678_CR5","unstructured":"J.-M. Chesneaux, Study of the computing accuracy by using probabilistic approach, in:Contribution to Computer Arithmetic and Self Validating Numerical Methods, ed. C. Ulrich (J.C. Baltzer, 1990) pp. 19\u201330."},{"key":"BF02140678_CR6","unstructured":"J.-M. Chesneaux, CADNA: An ADA tool for round-off error analysis and numerical debugging,Proc. Conf. ADA in Aerospace, Barcelona (December 1990)."},{"key":"BF02140678_CR7","unstructured":"J.-M. Chesneaux, Stochastic arithmetic properties, in:Computational and Applied Mathematics, I \u2014 Algorithms and Theory, ed. C. Brezinski (North-Holland, 1992) pp. 81\u201391."},{"key":"BF02140678_CR8","unstructured":"J.-M. Chesneaux, C.A.D.N.A.: Contr\u00f4le des arrondis et d\u00e9bogage num\u00e9rique en ADA, MASI Report, no. 92-31 (1992)."},{"key":"BF02140678_CR9","unstructured":"J.-M. Chesneaux, Descriptif d'utilisation du logiciel CADNA_F, MASI Report, no. 92.32 (1992)."},{"key":"BF02140678_CR10","first-page":"1435","volume":"315","author":"J.-M. Chesneaux","year":"1992","unstructured":"J.-M. Chesneaux and J. Vignes, Les fondements de l'arithm\u00e9tique stochastique, C.R. Acad. Sci., Paris, s\u00e9r. 1, 315 (1992) 1435\u20131440.","journal-title":"C.R. Acad. Sci., Paris, s\u00e9r. 1"},{"key":"BF02140678_CR11","first-page":"171","volume":"316","author":"J.-M. Chesneaux","year":"1993","unstructured":"J.-M. Chesneaux and J. Vignes, L'algorithme de Gauss en arithm\u00e9tique stochastique. C.R. Acad. Sci., Paris, s\u00e9r. II, 316 (1993) 171\u2013176.","journal-title":"C.R. Acad. Sci., Paris, s\u00e9r. II"},{"key":"BF02140678_CR12","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1145\/321941.321948","volume":"23","author":"a. Feldstein","year":"1976","unstructured":"a. Feldstein and R. Goodman, Convergence estimates for the distribution of trailing digits, J. ACM 23 (1976) 287\u2013297.","journal-title":"J. ACM"},{"key":"BF02140678_CR13","doi-asserted-by":"crossref","first-page":"1609","DOI":"10.1002\/j.1538-7305.1970.tb04281.x","volume":"9","author":"R.W. Hamming","year":"1970","unstructured":"R.W. Hamming, On the distribution of numbers, Bell Syst. Tech. J., 9 (1970) 1609\u20131625.","journal-title":"Bell Syst. Tech. J."},{"key":"BF02140678_CR14","doi-asserted-by":"crossref","unstructured":"T.E. Hull and J.R. Swenson, Test of probabilistic models for propagation of round-off errors, Commun. ACM 9 (1966).","DOI":"10.1145\/365170.365212"},{"key":"BF02140678_CR15","volume-title":"The Art of Computer Programming","author":"D.E. Knuth","year":"1969","unstructured":"D.E. Knuth,The Art of Computer Programming, vol. 2 (Addison-Wesley, Reading, 1969)."},{"key":"BF02140678_CR16","volume-title":"Algorithmes Num\u00e9riques, Analyse et Mise en Oeuvre","author":"J. Vignes","year":"1980","unstructured":"J. Vignes and M. La Porte,Algorithmes Num\u00e9riques, Analyse et Mise en Oeuvre, vol. 1 and 2 (Editions Technip, Paris, 1980)."},{"key":"BF02140678_CR17","unstructured":"J. Vignes and M. La Porte, Error analysis in computing, in:Information Processing 74 (North-Holland, 1974)."},{"key":"BF02140678_CR18","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/0378-4754(78)90016-2","volume":"20","author":"J. Vignes","year":"1978","unstructured":"J. Vignes, New methods for evaluating the validity of the results of mathematical computation, Math. Comp. Simul. 20 (1978) 221\u2013249.","journal-title":"Math. Comp. Simul."},{"key":"BF02140678_CR19","first-page":"1","volume":"4","author":"J. Vignes","year":"1987","unstructured":"J. Vignes, Z\u00e9ro math\u00e9matique et z\u00e9ro informatique, La Vie des Sciences, Comptes Rendus, s\u00e9rie g\u00e9n\u00e9rale, 4 (1987) 1\u201313.","journal-title":"Comptes Rendus, s\u00e9rie g\u00e9n\u00e9rale"},{"key":"BF02140678_CR20","first-page":"219","volume":"87","author":"J. Vignes","year":"1989","unstructured":"J. Vignes, Optimal implementation of optimization methods and estimation of the accuracy of the results, I.S.N.M. 87 (1989) 219\u2013227.","journal-title":"I.S.N.M."},{"key":"BF02140678_CR21","first-page":"93","volume":"7","author":"J. Vignes","year":"1990","unstructured":"J. Vignes, Estimation de la pr\u00e9cision des r\u00e9sultats de logiciels num\u00e9riques, La Vie des Sciences, Comptes Rendus, s\u00e9rie g\u00e9n\u00e9rale, 7 (1990) 93\u2013115.","journal-title":"Comptes Rendus, s\u00e9rie g\u00e9n\u00e9rale"},{"key":"BF02140678_CR22","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/0378-4754(93)90003-D","volume":"35","author":"J. Vignes","year":"1993","unstructured":"J. Vignes, A stochastic arithmetic for reliable scientific computation, Math. Comp. Simul. 35 (1993) 233\u2013261.","journal-title":"Math. Comp. Simul."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02140678.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02140678\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02140678","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,9]],"date-time":"2020-04-09T14:03:37Z","timestamp":1586441017000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02140678"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,9]]},"references-count":22,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1994,9]]}},"alternative-id":["BF02140678"],"URL":"https:\/\/doi.org\/10.1007\/bf02140678","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,9]]}}}