{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,22]],"date-time":"2026-02-22T23:00:57Z","timestamp":1771801257085,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":25,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642388552","type":"print"},{"value":"9783642388569","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-642-38856-9_1","type":"book-chapter","created":{"date-parts":[[2013,6,15]],"date-time":"2013-06-15T00:05:28Z","timestamp":1371254728000},"page":"1-3","source":"Crossref","is-referenced-by-count":17,"title":["Static Analysis by Abstract Interpretation of Numerical Programs and Systems, and FLUCTUAT"],"prefix":"10.1007","author":[{"given":"Eric","family":"Goubault","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"1_CR1","unstructured":"Adj\u00e9, A., Bouissou, O., Goubault-Larrecq, J., Goubault, E., Putot, S.: Analyzing probabilistic programs with partially known distributions. In: VSTTE (2013)"},{"key":"1_CR2","doi-asserted-by":"crossref","unstructured":"Adj\u00e9, A., Gaubert, S., Goubault, E.: Coupling policy iteration with semi-definite relaxation to compute accurate numerical invariants in static analysis. Logical Methods in Computer Science\u00a08(1) (2012)","DOI":"10.2168\/LMCS-8(1:1)2012"},{"key":"1_CR3","doi-asserted-by":"crossref","unstructured":"Boldo, S., Filli\u00e2tre, J.C.: Formal Verification of Floating-Point Programs. In: 18th IEEE International Symposium on Computer Arithmetic (June 2007)","DOI":"10.1109\/ARITH.2007.20"},{"key":"1_CR4","unstructured":"Bouissou, O., Conquet, E., Cousot, P., Cousot, R., Ghorbal, K., Lesens, D., Putot, S., Turin, M.: Space software validation using abstract interpretation. In: DASIA (2009)"},{"issue":"2-4","key":"1_CR5","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1007\/s00607-011-0182-8","volume":"94","author":"O. Bouissou","year":"2012","unstructured":"Bouissou, O., Goubault, E., Goubault-Larrecq, J., Putot, S.: A generalization of p-boxes to affine arithmetic. Computing\u00a094(2-4), 189\u2013201 (2012)","journal-title":"Computing"},{"key":"1_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"620","DOI":"10.1007\/978-3-642-02658-4_46","volume-title":"Computer Aided Verification","author":"O. Bouissou","year":"2009","unstructured":"Bouissou, O., Goubault, E., Putot, S., Tekkal, K., Vedrine, F.: HybridFluctuat: A static analyzer of numerical programs within a continuous environment. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol.\u00a05643, pp. 620\u2013626. Springer, Heidelberg (2009)"},{"key":"1_CR7","unstructured":"Comba, J.L.D., Stolfi, J.: Affine arithmetic and its applications to computer graphics. In: Proceedings of SIBGRAPI (1993)"},{"key":"1_CR8","doi-asserted-by":"crossref","unstructured":"Cousot, P., Cousot, R.: Abstract interpretation: A unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: POPL, pp. 238\u2013252 (1977)","DOI":"10.1145\/512950.512973"},{"key":"1_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1007\/978-3-642-04570-7_6","volume-title":"Formal Methods for Industrial Critical Systems","author":"D. Delmas","year":"2009","unstructured":"Delmas, D., Goubault, E., Putot, S., Souyris, J., Tekkal, K., V\u00e9drine, F.: Towards an industrial use of FLUCTUAT on safety-critical avionics software. In: Alpuente, M., Cook, B., Joubert, C. (eds.) FMICS 2009. LNCS, vol.\u00a05825, pp. 53\u201369. Springer, Heidelberg (2009)"},{"key":"1_CR10","doi-asserted-by":"crossref","unstructured":"Fajstrup, L., Goubault, \u00c9., Haucourt, E., Mimram, S., Raussen, M.: Trace spaces: An efficient new technique for state-space reduction. In: Seidl, H. (ed.) ESOP 2012. LNCS, vol.\u00a07211, pp. 274\u2013294. Springer, Heidelberg (2012)","DOI":"10.1007\/978-3-642-28869-2_14"},{"issue":"12","key":"1_CR11","doi-asserted-by":"publisher","first-page":"1416","DOI":"10.1016\/j.jsc.2011.12.048","volume":"47","author":"T.M. Gawlitza","year":"2012","unstructured":"Gawlitza, T.M., Seidl, H., Adj\u00e9, A., Gaubert, S., Goubault, E.: Abstract interpretation meets convex optimization. J. Symb. Comput.\u00a047(12), 1416\u20131446 (2012)","journal-title":"J. Symb. Comput."},{"key":"1_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"212","DOI":"10.1007\/978-3-642-14295-6_22","volume-title":"Computer Aided Verification","author":"K. Ghorbal","year":"2010","unstructured":"Ghorbal, K., Goubault, E., Putot, S.: A logical product approach to zonotope intersection. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol.\u00a06174, pp. 212\u2013226. Springer, Heidelberg (2010)"},{"key":"1_CR13","doi-asserted-by":"crossref","unstructured":"Goubault, E., Gall, T.L., Putot, S.: An accurate join for zonotopes, preserving affine input\/output relations. In: Proceedings of NSAD 2012, 4th Workshop on Numerical and Symbolic Abstract Domains. ENTCS, vol.\u00a0287, pp. 65\u201376 (2012)","DOI":"10.1016\/j.entcs.2012.09.007"},{"key":"1_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1007\/11823230_3","volume-title":"Static Analysis","author":"\u00c9. Goubault","year":"2006","unstructured":"Goubault, \u00c9., Putot, S.: Static analysis of numerical algorithms. In: Yi, K. (ed.) SAS 2006. LNCS, vol.\u00a04134, pp. 18\u201334. Springer, Heidelberg (2006)"},{"key":"1_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1007\/978-3-540-74061-2_9","volume-title":"Static Analysis","author":"E. Goubault","year":"2007","unstructured":"Goubault, E., Putot, S.: Under-approximations of computations in real numbers based on generalized affine arithmetic. In: Riis Nielson, H., Fil\u00e9, G. (eds.) SAS 2007. LNCS, vol.\u00a04634, pp. 137\u2013152. Springer, Heidelberg (2007)"},{"key":"1_CR16","unstructured":"Goubault, E., Putot, S.: A zonotopic framework for functional abstractions. CoRR abs\/0910.1763 (2009), \n                  \n                    http:\/\/arxiv.org\/abs\/0910.1763"},{"key":"1_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"232","DOI":"10.1007\/978-3-642-18275-4_17","volume-title":"Verification, Model Checking, and Abstract Interpretation","author":"E. Goubault","year":"2011","unstructured":"Goubault, E., Putot, S.: Static analysis of finite precision computations. In: Jhala, R., Schmidt, D. (eds.) VMCAI 2011. LNCS, vol.\u00a06538, pp. 232\u2013247. Springer, Heidelberg (2011)"},{"key":"1_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1007\/3-540-47764-0_14","volume-title":"Static Analysis","author":"\u00c9. Goubault","year":"2001","unstructured":"Goubault, \u00c9.: Static analyses of the precision of floating-point operations. In: Cousot, P. (ed.) SAS 2001. LNCS, vol.\u00a02126, pp. 234\u2013259. Springer, Heidelberg (2001)"},{"key":"1_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1007\/11539452_38","volume-title":"CONCUR 2005 \u2013 Concurrency Theory","author":"E. Goubault","year":"2005","unstructured":"Goubault, E., Haucourt, E.: A practical application of geometric semantics to static analysis of concurrent programs. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol.\u00a03653, pp. 503\u2013517. Springer, Heidelberg (2005)"},{"key":"1_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/978-3-540-79707-4_3","volume-title":"Formal Methods for Industrial Critical Systems","author":"E. Goubault","year":"2008","unstructured":"Goubault, E., Putot, S., Baufreton, P., Gassino, J.: Static analysis of the accuracy in control systems: Principles and experiments. In: Leue, S., Merino, P. (eds.) FMICS 2007. LNCS, vol.\u00a04916, pp. 3\u201320. Springer, Heidelberg (2008)"},{"key":"1_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1007\/978-3-642-33125-1_5","volume-title":"Static Analysis","author":"E. Goubault","year":"2012","unstructured":"Goubault, E., Putot, S., V\u00e9drine, F.: Modular static analysis with zonotopes. In: Min\u00e9, A., Schmidt, D. (eds.) SAS 2012. LNCS, vol.\u00a07460, pp. 24\u201340. Springer, Heidelberg (2012)"},{"key":"1_CR22","unstructured":"Menard, D., Rocher, R., Sentieys, O., Simon, N., Didier, L.S., Hilaire, T., Lopez, B., Goubault, E., Putot, S., V\u00e9drine, F., Najahi, A., Revy, G., Fangain, L., Samoyeau, C., Lemonnier, F., Clienti, C.: Design of fixed-point embedded systems (defis) french anr project. In: DASIP, pp. 1\u20132 (2012)"},{"key":"1_CR23","doi-asserted-by":"crossref","unstructured":"Meurant, G.: The Lanczos and Conjugate Gradient Algorithms: From Theory to Finite Precision Computations (Software, Environments, and Tools). SIAM (2006)","DOI":"10.1137\/1.9780898718140"},{"key":"1_CR24","unstructured":"Paige, C.C.: The computation of eigenvalues and eigenvectors of very large sparse matrices. Ph.D. thesis (1971)"},{"key":"1_CR25","unstructured":"Wilkinson, J.H.: The algebraic eigenvalue problem. Oxford University Press (1965)"}],"container-title":["Lecture Notes in Computer Science","Static Analysis"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-38856-9_1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,14]],"date-time":"2019-05-14T00:50:07Z","timestamp":1557795007000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-38856-9_1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783642388552","9783642388569"],"references-count":25,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-38856-9_1","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}