{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,6,29]],"date-time":"2023-06-29T19:40:54Z","timestamp":1688067654711},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2013,2,26]],"date-time":"2013-02-26T00:00:00Z","timestamp":1361836800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2013,8]]},"DOI":"10.1007\/s00500-013-1014-x","type":"journal-article","created":{"date-parts":[[2013,2,25]],"date-time":"2013-02-25T11:52:47Z","timestamp":1361793167000},"page":"1453-1465","source":"Crossref","is-referenced-by-count":1,"title":["An overview of C-XSC as a tool for interval arithmetic and its application in computing verified uncertain probabilistic models under Dempster\u2013Shafer theory"],"prefix":"10.1007","volume":"17","author":[{"given":"Michael","family":"Zimmer","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gabor","family":"Rebner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Walter","family":"Kr\u00e4mer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,2,26]]},"reference":[{"key":"1014_CR3","doi-asserted-by":"crossref","unstructured":"Anderson E, Bai Z, Bischof C, Blackford S, Demmel J, Dongarra J, Croz JD, Greenbaum A, Hammarling S, McKenney A, Sorensen D (1999) LAPACK Users\u2019 Guide, 3rd edn. Society for Industrial and Applied Mathematics, Philadelphia","DOI":"10.1137\/1.9780898719604"},{"key":"1014_CR4","doi-asserted-by":"crossref","unstructured":"Auer E, Luther W (2009) Numerical verification assessment in computational biomechanics. In: Proceedings of Dagstuhl seminar 08021. Numerical validation in current hardware architectures. Lecture notes in computer science, vol 5492. Springer, Berlin\/Heidelberg, pp 145\u2013160. doi: 10.1007\/978-3-642-01591-5_9","DOI":"10.1007\/978-3-642-01591-5_9"},{"key":"1014_CR5","unstructured":"Auer E, Luther W, Rebner G, Limbourg P (2010) A Verified MATLAB Toolbox for the Dempster\u2013Shafer Theory. In: Proceedings of the workshop on the theory of belief functions. http:\/\/www.ensieta.fr\/belief2010\/papers\/p83.pdf , http:\/\/www.udue.de\/DSI"},{"issue":"2","key":"1014_CR6","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1145\/567806.567807","volume":"28","author":"L Blackford","year":"2002","unstructured":"Blackford L, Demmel J, Dongarra J, Duff I, Hammarling S, Henry G, Heroux M, Kaufman L, Lumsdaine A, Petitet A, Pozo R, Remington K, Whaley R (2002) An updated set of basic linear algebra subprograms (BLAS). ACM Trans Math Soft 28(2):135\u2013151","journal-title":"ACM Trans Math Soft"},{"key":"1014_CR7","unstructured":"Blomquist F, Kr\u00e4mer W, Hofschuster W (2005) Real and complex Taylor arithmetic in C-XSC. BUW-WRSWT (preprints 2005(3))"},{"key":"1014_CR8","doi-asserted-by":"crossref","unstructured":"Boisvert RF, Pozo R, Remington KA (1996) The matrix market exchange formats: initial design. Tech. Rep. 5935, NIST Interim Report. http:\/\/math.nist.gov\/MatrixMarket\/","DOI":"10.6028\/NIST.IR.5935"},{"key":"1014_CR9","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1214\/aoms\/1177698950","volume":"38","author":"A Dempster","year":"1967","unstructured":"Dempster A (1967) Upper and lower probabilities induced by a multivalued mapping. Annals Math Stat 38:325\u2013339","journal-title":"Annals Math Stat"},{"key":"1014_CR10","doi-asserted-by":"crossref","unstructured":"Ferson S, Kreinovich V, Ginzburg L, Myers D, Sentz K (2003) Constructing Probability boxes and Dempster\u2013Shafer structures. SAND2002-4015. Sandia National Laboratories, Albuquerque","DOI":"10.2172\/809606"},{"key":"1014_CR11","doi-asserted-by":"crossref","unstructured":"Gilbert JR, Moler C, Schreiber R (1992) Sparse matrices in Matlab: design and implementation. SIAM J Matrix Anal Appl 30(1):333\u2013356","DOI":"10.1137\/0613024"},{"key":"1014_CR12","unstructured":"Grimmer M (2005) An MPI Extension for the use of C-XSC in parallel environments. BUW-WRSWT (preprints 2005(3))"},{"key":"1014_CR13","unstructured":"Hammer R, Hocks M, Kulisch U, Ratz D (1995) C++ Toolbox for verified computing. Springer, Heidelberg"},{"key":"1014_CR14","unstructured":"Hofschuster W, Kr\u00e4mer H (2004) C-XSC 2.0: a C++ library for extended scientific computing. In: Lecture Notes in Computer Science, vol 2991\/2004. Springer, Heidelberg, pp 15\u201335"},{"key":"1014_CR15","doi-asserted-by":"crossref","unstructured":"Institute of Electrical and Electronics Engineers (2008) IEEE Standard for Floating-Point Arithmetic. IEEE Std 754-2008,\u00a0pp 1\u201358. doi: 10.1109\/IEEESTD.2008.4610935","DOI":"10.1109\/IEEESTD.2008.4610935"},{"key":"1014_CR16","doi-asserted-by":"crossref","unstructured":"Klatte R, Kulisch U, Wiethoff A, Lawo C, Rauch M (1993) C-XSC - A C++ class library for extended scientific computing. Springer, Heidelberg","DOI":"10.1007\/978-3-642-58058-1"},{"issue":"3","key":"1014_CR17","first-page":"193","volume":"15","author":"M Kolberg","year":"2011","unstructured":"Kolberg M, Kr\u00e4mer W, Zimmer M (2011) Efficient parallel solvers for large dense systems of linear interval equations. Reliable Comput 15(3):193\u2013206","journal-title":"Reliable Comput"},{"key":"1014_CR18","unstructured":"Kr\u00e4mer W (2010) High performance verified computing using C-XSC. In: Reiser R, Pilla L (eds) IntMath-TSD: interval mathematics and connections in teaching and scientific development. Universidade Federal de Pelotas, Ed. Universit\u00e1ria, pp 3\u201314"},{"issue":"2","key":"1014_CR19","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/s00607-011-0174-8","volume":"94","author":"W Kr\u00e4mer","year":"2012","unstructured":"Kr\u00e4mer W. (2012) Multiple\/arbitrary precision interval computations in C-XSC. Computing 94(2):229\u2013241","journal-title":"Computing"},{"key":"1014_CR20","unstructured":"Kr\u00e4mer W, Blomquist F (2000) Reliable computation of the error function and the complementary error function. BUW-WRSWT (preprints 2000(2))"},{"key":"1014_CR21","doi-asserted-by":"crossref","unstructured":"Kr\u00e4mer W, Zimmer M (2009) Fast (Parallel) dense linear system solvers in C-XSC using error free transformations and BLAS. In: Cuyt E, Kra\u00e4mer W, Luther W, Markstein P (eds) Lecture Notes in computer science LNCS, vol 5492. Numerical validation in current hardware architectures. Springer, Heidelberg, pp 320\u2013349","DOI":"10.1007\/978-3-642-01591-5_15"},{"key":"1014_CR22","doi-asserted-by":"crossref","unstructured":"Kreinovich V (2008) Relations between interval computing and soft computing. Tech. Rep. 86, Departmental Technical Reports (CS). http:\/\/digitalcommons.utep.edu\/cs_techrep\/86","DOI":"10.1007\/978-1-84800-326-2_3"},{"key":"1014_CR23","unstructured":"Kulisch U (1997) Die f\u00fcnfte Gleitkommaoperation f\u00fcr Top-Performance Computer. Berichte aus dem Forschungsschwerpunkt Computerarithmetik, Intervallrechnung und numerische Algorithmen mit Ergebnisverifikation. Universit\u00e4t Karlsruhe"},{"key":"1014_CR24","doi-asserted-by":"crossref","unstructured":"Kulisch U (2008) Computer arithmetic and validity: Theory, implementation, and applications. Walter de Gruyter, Berlin","DOI":"10.1515\/9783110203196"},{"key":"1014_CR25","doi-asserted-by":"crossref","unstructured":"Kulisch U, Miranker W (1986) The arithmetic of the digital computer: a new approach. SIAM Rev 28, 1\u201340. doi: 10.1137\/1028001 . http:\/\/portal.acm.org\/citation.cfm?id=13139.13140","DOI":"10.1137\/1028001"},{"key":"1014_CR26","unstructured":"Li X, Demmel J, Bailey D, Hida G, Iskandar J, Kahan W, Martin M, Tung T, Yoo D (2000) Design, implementation, and testing of extended and MixedPrecision BLAS. Tech. Rep. CS\u201300\u2013451, University of Tennessee. http:\/\/citeseer.nj.nec.com\/li00design.html (submitted to ACM TOMS)"},{"key":"1014_CR27","unstructured":"Limbourg P (2007) Imprecise probabilities for predicting dependability of mechatronic systems in early design stages. Ph.D. thesis, Universit\u00e4t Dusburg-Essen"},{"key":"1014_CR28","doi-asserted-by":"crossref","unstructured":"Lohner R (1993) Interval arithmetic in staggered correction format. In: Adams E, Kulisch U (eds) Scientific computing with automatic result verification. Academic Press, San Diego, pp 301\u2013321","DOI":"10.1016\/S0076-5392(08)62850-7"},{"key":"1014_CR29","doi-asserted-by":"crossref","unstructured":"Ogita T, Rump SM, Oish S (2005) Accurate sum and dot product. SIAM J Sci Comput 26(6):1955\u20131988","DOI":"10.1137\/030601818"},{"key":"1014_CR30","unstructured":"OpenMP (2011) Architecture review board: OpenMP application programming interface 3.1"},{"key":"1014_CR31","doi-asserted-by":"crossref","unstructured":"Popova E (2009) Mathematica connectivity to interval libraries filib++ and C-XSC. Numerical validation, Lecture notes in computer science, vol 5492. Springer, Berlin\/Heidelberg, pp 117\u2013132","DOI":"10.1007\/978-3-642-01591-5_7"},{"key":"1014_CR32","doi-asserted-by":"crossref","unstructured":"Popova ED, Kr\u00e4mer W (2010) Communicating functional expressions from mathematica to C-XSC. In: Proceedings of the third international congress conference on mathematical software ICMS'10, Kobe, Japan. Springer, Berlin\/Heidelberg, pp 354\u2013365. ISBN 3-642-15581-2, 978-3-642-15581-9. http:\/\/dl.acm.org\/citation.cfm?id=1888390.1888465","DOI":"10.1007\/978-3-642-15582-6_56"},{"key":"1014_CR33","doi-asserted-by":"crossref","unstructured":"Rebner G, Auer E, Luther W (2012) A verified realization of a Dempster\u2013Shafer-based fault tree analysis. Computing 94:313\u2013324. doi: 10.1007\/s00607-011-0179-3","DOI":"10.1007\/s00607-011-0179-3"},{"key":"1014_CR34","doi-asserted-by":"crossref","unstructured":"Rump S (1999) INTLAB\u2014INTERVAL LABORATORY. In: Developments in reliable computing, vol 1. Kluwer Academic Publishers, Dordrecht, pp 77\u2013104. http:\/\/www.ti3.tu-harburg.de\/","DOI":"10.1007\/978-94-017-1247-7_7"},{"key":"1014_CR35","doi-asserted-by":"crossref","unstructured":"Schweizer W (2009) MATLAB kompakt, 4th edn. Oldenbourg, M\u00fcnchen","DOI":"10.1524\/9783486710687"},{"key":"1014_CR36","unstructured":"Shafer G (1976) A mathematical theory of evidence. Princeton University Press, Princeton"},{"key":"1014_CR1","unstructured":"Weblink to C-XSC (2013) http:\/\/www.xsc.de\/"},{"key":"1014_CR2","unstructured":"Weblink to SuiteSparse (2013) http:\/\/www.cise.ufl.edu\/research\/sparse\/SuiteSparse"},{"key":"1014_CR37","unstructured":"Wolfram S (2004) The Mathematica Book. Wolfram Media, Cambridge. ISBN 1-57955-022-3"},{"key":"1014_CR38","unstructured":"Zimmer M (2011) Using C-XSC in a multi-threaded environment. BUW WRSWT (preprints 2011(2))"},{"key":"1014_CR39","doi-asserted-by":"crossref","unstructured":"Zimmer M, Kr\u00e4mer W, Bohlender G, Hofschuster W (2010) Extension of the C-XSC library with scalar products with selectable accuracy. Serdica J Comput (Preprint \u2013 BUW-WRSWT 2009\/4)","DOI":"10.55630\/sjc.2010.4.349-370"},{"issue":"1","key":"1014_CR40","first-page":"138","volume":"14","author":"M Zimmer","year":"2010","unstructured":"Zimmer M, Kr\u00e4mer W, Hofschuster W (2010) Sparse matrices and vectors in C-XSC. Reliable Comput 14(1):138\u2013160","journal-title":"Reliable Comput"},{"issue":"2","key":"1014_CR41","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/s00607-011-0170-z","volume":"94","author":"M Zimmer","year":"2012","unstructured":"Zimmer M, Kr\u00e4mer W, Popova E (2012) Solvers for the verified solution of parametric linear systems. Computing 94(2):109\u2013123","journal-title":"Computing"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-013-1014-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00500-013-1014-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-013-1014-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,29]],"date-time":"2023-06-29T19:02:47Z","timestamp":1688065367000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00500-013-1014-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,2,26]]},"references-count":41,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2013,8]]}},"alternative-id":["1014"],"URL":"https:\/\/doi.org\/10.1007\/s00500-013-1014-x","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,2,26]]}}}