{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T04:57:39Z","timestamp":1777611459086,"version":"3.51.4"},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[1985,12,1]],"date-time":"1985-12-01T00:00:00Z","timestamp":502243200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computing"],"published-print":{"date-parts":[[1985,12]]},"DOI":"10.1007\/bf02251834","type":"journal-article","created":{"date-parts":[[2005,11,15]],"date-time":"2005-11-15T08:19:43Z","timestamp":1132042783000},"page":"349-364","source":"Crossref","is-referenced-by-count":9,"title":["Probabilistic error analysis of gaussian elimination in floating point and logarithmic arithmetic","Stochastische Fehleranalyse des Gau\u00dfschen Eliminationsverfahrens in Gleitkomma- und logarithmischer Arithmetik"],"prefix":"10.1007","volume":"34","author":[{"given":"J. L.","family":"Barlow","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"E. H.","family":"Bareiss","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"BF02251834_CR1","unstructured":"Bareiss, E. H., Grau, A. A.: Basics of the CRD computer. Northwestern University ERDA Report COO-2280-35, Evanston, Illinois (August, 1977)."},{"key":"BF02251834_CR2","volume-title":"Probabilistic error analysis of floating point and CRD arthmetics","author":"J. L. Barlow","year":"1981","unstructured":"Barlow, J. L.: Probabilistic error analysis of floating point and CRD arthmetics. Ph. D. Thesis, Northwestern University, Evanston, Illinois (June 1981)."},{"key":"BF02251834_CR3","volume-title":"Fast a posteriori bounds for roundoff error in Gaussian elimination","author":"J. L. Barlow","year":"1983","unstructured":"Barlow, J. L. Fast a posteriori bounds for roundoff error in Gaussian elimination. Technical Report No. CS-83-20, Department of Computer Science, The Pennsylvania State University, University Park, Pennsylvania (September 1983)."},{"key":"BF02251834_CR4","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/BF02251833","volume":"34","author":"J. L. Barlow","year":"1985","unstructured":"Barlow, J. L., Bareiss, E. H.: On roundoff error distributions in floating point and logarithmic arithmetic. Computing34, 325\u2013347 (1985).","journal-title":"Computing"},{"key":"BF02251834_CR5","volume-title":"Probabilistic error analysis of Gaussian elimination in floating point and logarithmic arithmetic","author":"J. L. Barlow","year":"1984","unstructured":"Barlow, J. L., Bareiss, E. H.: Probabilistic error analysis of Gaussian elimination in floating point and logarithmic arithmetic. Technical Report No. CS-84-21, Department of Computer Science, The Pennsylvania State University, University Park, Pennsylvania (December 1984)."},{"key":"BF02251834_CR6","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1145\/322154.322162","volume":"26","author":"J. Bustoz","year":"1979","unstructured":"Bustoz, J., Feldstein, A., Goodman, R., Linnaimaa, S.: Improved trailing digit estimates applied to optimal computer Arithmetic. JACM26, 716\u2013730 (1979).","journal-title":"JACM"},{"key":"BF02251834_CR7","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1145\/62.322429","volume":"31","author":"C. W. Clenshaw","year":"1984","unstructured":"Clenshaw, C. W., Olver, F. W. J.: Beyond floating point. JACM31, 319\u2013328 (1984).","journal-title":"JACM"},{"issue":"4","key":"BF02251834_CR8","first-page":"328","volume":"31","author":"R. Goodman","year":"1983","unstructured":"Goodman, R., Feldstein, A.: Loss of significance in floating point subtraction and addition. IEEE Trans. on ComputersC-31 (4), 328\u2013335 (1983).","journal-title":"IEEE Trans. on Computers C"},{"key":"BF02251834_CR9","volume-title":"Introduction to mathematical statistics","author":"R. V. Hogg","year":"1970","unstructured":"Hogg, R. V., Craig, A. T.: Introduction to mathematical statistics, third edition. New York: Macmillan 1970.","edition":"third edition"},{"key":"BF02251834_CR10","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1137\/0715024","volume":"15","author":"F. W. J. Olver","year":"1978","unstructured":"Olver, F. W. J.: A new approach to error arthmetic. SIAM J. Num. Anal.15, 368\u2013393 (1978).","journal-title":"SIAM J. Num. Anal."},{"key":"BF02251834_CR11","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1093\/imanum\/2.4.377","volume":"2","author":"F. W. J. Olver","year":"1982","unstructured":"Olver, F. W. J., Wilkinson, J. H.: A posteriori error bounds for Gaussian elimination. IMA J. Num. Anal.2, 377\u2013406 (1982).","journal-title":"IMA J. Num. Anal."},{"key":"BF02251834_CR12","first-page":"374","volume":"8","author":"J. K. Reid","year":"1971","unstructured":"Reid, J. K.: A note on the stability of Gaussian elimination. JIMA8, 374\u2013375 (1971).","journal-title":"JIMA"},{"key":"BF02251834_CR13","first-page":"409","volume":"20","author":"H. H. Robertson","year":"1977","unstructured":"Robertson, H. H.: The accuracy of error estimates for systems of linear algebraic equations. JIMA20, 409\u2013414 (1977).","journal-title":"JIMA"},{"issue":"No. 11","key":"BF02251834_CR14","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.1090\/S0002-9904-1947-08909-6","volume":"53","author":"J. Neumann Von","year":"1947","unstructured":"Von Neumann, J., Goldstine, H. H.: Numerical inversion of matrices of high order. Bulletin of the AMS53, No. 11, 1021\u20131099 (1947).","journal-title":"Bulletin of the AMS"},{"key":"BF02251834_CR15","volume-title":"The Algebraic Eigenvalue Problem","author":"J. H. Wilkinson","year":"1965","unstructured":"Wilkinson, J. H.: The Algebraic Eigenvalue Problem. Oxford: Clarendon Press 1965."},{"key":"BF02251834_CR16","volume-title":"Rounding Errors in Algebraic Processes","author":"J. H. Wilkinson","year":"1963","unstructured":"Wilkinson, J. H.: Rounding Errors in Algebraic Processes. Englewood Cliffs, N. J.: Prentice-Hall 1963."}],"container-title":["Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02251834.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02251834\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02251834","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T10:46:03Z","timestamp":1558003563000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02251834"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1985,12]]},"references-count":16,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1985,12]]}},"alternative-id":["BF02251834"],"URL":"https:\/\/doi.org\/10.1007\/bf02251834","relation":{},"ISSN":["0010-485X","1436-5057"],"issn-type":[{"value":"0010-485X","type":"print"},{"value":"1436-5057","type":"electronic"}],"subject":[],"published":{"date-parts":[[1985,12]]}}}