{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T07:21:01Z","timestamp":1757575261301},"reference-count":14,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[1989,6,1]],"date-time":"1989-06-01T00:00:00Z","timestamp":612662400000},"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":[[1989,6]]},"DOI":"10.1007\/bf02241860","type":"journal-article","created":{"date-parts":[[2005,11,14]],"date-time":"2005-11-14T19:34:05Z","timestamp":1131996845000},"page":"171-185","source":"Crossref","is-referenced-by-count":5,"title":["Root squaring using level-index arithmetic"],"prefix":"10.1007","volume":"43","author":[{"given":"C. W.","family":"Clenshaw","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P. R.","family":"Turner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"BF02241860_CR1","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1145\/62.322429","volume":"31","author":"C. W. Clenshaw","year":"1984","unstructured":"C. W. Clenshaw and F. W. J. Olver, Beyond floating-point, J ACM31, (1984) 319\u2013328.","journal-title":"J ACM"},{"key":"BF02241860_CR2","doi-asserted-by":"crossref","first-page":"470","DOI":"10.1137\/0724034","volume":"24","author":"C. W. Clenshaw","year":"1987","unstructured":"C. W. Clenshaw and F. W. J. Olver, Level-index arithmetic operations, SIAM J on Num Anal24 (1987) 470\u2013485.","journal-title":"SIAM J on Num Anal"},{"key":"BF02241860_CR3","series-title":"Lecture Notes in Mathematics","first-page":"95","volume-title":"Numerical Analysis, and Parallel Processing","author":"C. W. Clenshaw","year":"1989","unstructured":"C. W. Clenshaw, F. W. J. Olver and P. R. Turner, Level-index arithmetic: An introductory Survey, Numerical Analysis, and Parallel Processing, (P. R. Turner, Ed.) 95\u2013168. Springer, Berlin-Heidelberg-New York-Tokyo-Hong Kong: Lecture Notes in Mathematics 1397, 1989."},{"key":"BF02241860_CR4","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1093\/imanum\/8.4.517","volume":"8","author":"C. W. Clenshaw","year":"1988","unstructured":"C. W. Clenshaw and P. R. Turner, The symmetric level-index system, IMA J Num Anal,8 (1988) 517\u2013526.","journal-title":"IMA J Num Anal"},{"key":"BF02241860_CR5","volume-title":"Applied and Computational Complex Analysis, Vol III","author":"P. Henrici","year":"1986","unstructured":"P. Henrici, Applied and Computational Complex Analysis, Vol III, Wiley, London, 1986."},{"key":"BF02241860_CR6","unstructured":"D. W. Lozier and F. W. J. Olver, Closure and precision in computer arithmetic, Manuscript."},{"key":"BF02241860_CR7","first-page":"123","volume":"4","author":"S. Matsui","year":"1981","unstructured":"S. Matsui and M. Iri, An overflow\/underflow-free floating-point representation of numbers, J Inf Proc4 (1981) 123\u2013133.","journal-title":"J Inf Proc"},{"key":"BF02241860_CR8","first-page":"1678","volume":"20","author":"R. Morris","year":"1973","unstructured":"R. Morris, Tapered floating-point: A new floating-point representation, IEEE Trans on Computers20 (1973) 1678\u20131679.","journal-title":"IEEE Trans on Computers"},{"key":"BF02241860_CR9","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1098\/rsta.1952.0010","volume":"244","author":"F. W. J. Olver","year":"1952","unstructured":"F. W. J. Olver, The evaluation of zeros of high-degree polynomials, Phil Trans Royal Soc A 244 (1952) 385\u2013415.","journal-title":"Phil Trans Royal Soc A"},{"key":"BF02241860_CR10","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1137\/0715024","volume":"15","author":"F. W. J. Olver","year":"1978","unstructured":"F. W. J. Olver, A new approach to error arithmetic, SIAM J Num Anal15, (1978) 368\u2013393.","journal-title":"SIAM J Num Anal"},{"key":"BF02241860_CR11","first-page":"144","volume-title":"Proc ARITH 8","author":"F. W. J. Olver","year":"1987","unstructured":"F. W. J. Olver and P. R. Turner, Implementation of level-index arithmetic using partial table look-up, Proc ARITH 8 (M. J. Irwin and R. Stefanelli, Eds.) pp. 144\u2013147, IEEE Computer Society, Washington DC, 1987."},{"key":"BF02241860_CR12","volume-title":"A first course in numerical analysis","author":"A. Ralston","year":"1965","unstructured":"A. Ralston, A first course in numerical analysis, McGraw-Hill, New York, 1965."},{"key":"BF02241860_CR13","first-page":"188","volume":"22","author":"P. R. Turner","year":"1986","unstructured":"P. R. Turner, Towards a fast implementation of level-index arithmetic, Bull IMA22 (1986) 188\u2013191.","journal-title":"Bull IMA"},{"key":"BF02241860_CR14","series-title":"Notes on Applied Science","volume-title":"Rounding errors in numerical processes","author":"J. H. Wilkinson","year":"1963","unstructured":"J. H. Wilkinson, Rounding errors in numerical processes, National Physical Lab., Notes on Applied Science, HMSO, London, 1963."}],"container-title":["Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02241860.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02241860\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02241860","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,14]],"date-time":"2019-05-14T23:15:48Z","timestamp":1557875748000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02241860"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,6]]},"references-count":14,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1989,6]]}},"alternative-id":["BF02241860"],"URL":"https:\/\/doi.org\/10.1007\/bf02241860","relation":{},"ISSN":["0010-485X","1436-5057"],"issn-type":[{"value":"0010-485X","type":"print"},{"value":"1436-5057","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989,6]]}}}