{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T21:51:01Z","timestamp":1761947461585,"version":"3.41.0"},"publisher-location":"New York, NY, USA","reference-count":29,"publisher":"ACM","license":[{"start":{"date-parts":[[2007,7,29]],"date-time":"2007-07-29T00:00:00Z","timestamp":1185667200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2007,7,29]]},"DOI":"10.1145\/1277548.1277577","type":"proceedings-article","created":{"date-parts":[[2007,12,7]],"date-time":"2007-12-07T19:19:41Z","timestamp":1197055181000},"page":"203-210","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":18,"title":["On exact and approximate interpolation of sparse rational functions"],"prefix":"10.1145","author":[{"given":"Erich","family":"Kaltofen","sequence":"first","affiliation":[{"name":"North Carolina State University, Raleigh, North Carolina"}]},{"given":"Zhengfeng","family":"Yang","sequence":"additional","affiliation":[{"name":"North Carolina State University, Raleigh, North Carolina"}]}],"member":"320","published-online":{"date-parts":[[2007,7,29]]},"reference":[{"key":"e_1_3_2_1_1_1","series-title":"Lect","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1007\/978-3-540-24588-9_22","volume-title":"Large-Scale Scientific Computing (Heidelberg","author":"Becuwe S.","year":"2004","unstructured":"Becuwe , S. , Cuyt , A. , and Verdonk , B . Multivariate rational interpolation of scattered data . In Large-Scale Scientific Computing (Heidelberg , Germany, 2004 ), I. Lirkov, S. Margenov, J. Wasniewski, and Y. Plamen, Eds., vol. 2907 of Lect . Notes Comput. Sci., Springer Verlag , pp. 204 -- 213 . Becuwe, S., Cuyt, A., and Verdonk, B. Multivariate rational interpolation of scattered data. In Large-Scale Scientific Computing (Heidelberg, Germany, 2004), I. Lirkov, S. Margenov, J. Wasniewski, and Y. Plamen, Eds., vol. 2907 of Lect. Notes Comput. Sci., Springer Verlag, pp. 204--213."},{"key":"e_1_3_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/62212.62241"},{"key":"e_1_3_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(78)90067-4"},{"key":"e_1_3_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/281508.281538"},{"key":"e_1_3_2_1_5_1","volume-title":"Ed. ISSAC MMVI Proc. 2006 Internat. Symp. Symbolic Algebraic Comput.","author":"Dumas J.-G.","year":"2006","unstructured":"Dumas , J.-G. Ed. ISSAC MMVI Proc. 2006 Internat. Symp. Symbolic Algebraic Comput. ( New York, N.Y. , 2006 ), ACM Press. Dumas, J.-G. Ed. ISSAC MMVI Proc. 2006 Internat. Symp. Symbolic Algebraic Comput. (New York, N.Y., 2006), ACM Press."},{"key":"e_1_3_2_1_6_1","volume-title":"Modern Computer Algebra","author":"von zur Gathen J.","year":"1999","unstructured":"von zur Gathen , J. , and Gerhard , J . Modern Computer Algebra . Cambridge University Press , Cambridge, New York, Melbourne, 1999 . Second edition 2003. von zur Gathen, J., and Gerhard, J. Modern Computer Algebra. Cambridge University Press, Cambridge, New York, Melbourne, 1999. Second edition 2003."},{"key":"e_1_3_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/1145768.1145792"},{"key":"e_1_3_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539791194069"},{"key":"e_1_3_2_1_9_1","first-page":"47","volume-title":"Wang and Zhi {26}","author":"Kai H.","unstructured":"Kai , H. Rational function approximation and its ill-conditioned property . In Wang and Zhi {26} , pp. 47 -- 53 . Preliminary version in {25}, pp. 62--64. Kai, H. Rational function approximation and its ill-conditioned property. In Wang and Zhi {26}, pp.47--53. Preliminary version in {25}, pp. 62--64."},{"key":"e_1_3_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/42267.45069"},{"key":"e_1_3_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/190347.190431"},{"key":"e_1_3_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.2307\/2153451"},{"key":"e_1_3_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0747-7171(03)00088-9"},{"key":"e_1_3_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/345542.345629"},{"key":"e_1_3_2_1_15_1","first-page":"188","article-title":"Computing greatest common divisors and factorizations in quadratic number fields","volume":"53","author":"Kaltofen E.","year":"1989","unstructured":"Kaltofen , E. , and Rolletschek , H . Computing greatest common divisors and factorizations in quadratic number fields . Math. Comput. 53 , 188 ( 1989 ), 697--720. Kaltofen, E., and Rolletschek, H. Computing greatest common divisors and factorizations in quadratic number fields. Math. Comput. 53,188 (1989), 697--720.","journal-title":"Math. Comput."},{"key":"e_1_3_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0747-7171(08)80015-6"},{"key":"e_1_3_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/1145768.1145799"},{"key":"e_1_3_2_1_18_1","volume-title":"On probabilistic analysis of randomization in hybrid symbolic-numeric algorithms","author":"Kaltofen E.","year":"2007","unstructured":"Kaltofen , E. , Yang , Z. , and Zhi , L . On probabilistic analysis of randomization in hybrid symbolic-numeric algorithms , 2007 . Manuscript in preparation. Kaltofen, E., Yang, Z., and Zhi, L. On probabilistic analysis of randomization in hybrid symbolic-numeric algorithms, 2007. Manuscript in preparation."},{"key":"e_1_3_2_1_19_1","first-page":"69","volume-title":"Wang and Zhi {26}","author":"Kaltofen E.","unstructured":"Kaltofen , E. , Yang , Z. , and Zhi , L . Structured low rank approximation of a Sylvester matrix . In Wang and Zhi {26} , pp. 69 -- 83 . Preliminary version in {25 }, pp. 188--201. Kaltofen, E., Yang, Z., and Zhi, L. Structured low rank approximation of a Sylvester matrix. In Wang and Zhi {26}, pp.69--83. Preliminary version in {25 }, pp. 188--201."},{"key":"e_1_3_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1137\/0214016"},{"key":"e_1_3_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/1005285.1005321"},{"key":"e_1_3_2_1_22_1","volume-title":"Sept.","author":"Olesh Z.","year":"2006","unstructured":"Olesh , Z. , and Storjohann , A . The vector rational function reconstruction problem , Sept. 2006 . Manuscript , 14 pages. Olesh, Z., and Storjohann, A. The vector rational function reconstruction problem, Sept. 2006. Manuscript, 14 pages."},{"key":"e_1_3_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022347425533"},{"key":"e_1_3_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/322217.322225"},{"volume-title":"Eds. Internat. Workshop on Symbolic-Numeric Comput. SNC 2005 Proc.(2005). Distributed at the Workshop in Xi'an, China, July 19-21","author":"Wang D.","key":"e_1_3_2_1_25_1","unstructured":"Wang , D. , and Zhi , L . Eds. Internat. Workshop on Symbolic-Numeric Comput. SNC 2005 Proc.(2005). Distributed at the Workshop in Xi'an, China, July 19-21 . Wang, D., and Zhi, L. Eds. Internat. Workshop on Symbolic-Numeric Comput. SNC 2005 Proc.(2005). Distributed at the Workshop in Xi'an, China, July 19-21."},{"key":"e_1_3_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.5555\/1204417"},{"key":"e_1_3_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/1089292.1089293"},{"key":"e_1_3_2_1_28_1","series-title":"Lect","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1007\/3-540-09519-5_73","volume-title":"Symbolic and Algebraic Computation (Heidelberg","author":"Zippel R.","year":"1979","unstructured":"Zippel , R. Probabilistic algorithms for sparse polynomials . In Symbolic and Algebraic Computation (Heidelberg , Germany, 1979 ), vol. 72 of Lect . Notes Comput. Sci., Springer Verlag , pp. 216 -- 226 . Proc. EUROSAM '79. Zippel, R. Probabilistic algorithms for sparse polynomials. In Symbolic and Algebraic Computation (Heidelberg, Germany, 1979), vol. 72 of Lect. Notes Comput. Sci., Springer Verlag, pp.216--226. Proc. EUROSAM '79."},{"key":"e_1_3_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0747-7171(08)80018-1"}],"event":{"name":"ISSAC07: International Symposium on Symbolic and Algebraic Computation","sponsor":["ACM Association for Computing Machinery","SIGSAM ACM Special Interest Group on Symbolic and Algebraic Manipulation"],"location":"Waterloo Ontario Canada","acronym":"ISSAC07"},"container-title":["Proceedings of the 2007 international symposium on Symbolic and algebraic computation"],"original-title":[],"link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1277548.1277577","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1277548.1277577","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T14:58:13Z","timestamp":1750258693000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1277548.1277577"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,7,29]]},"references-count":29,"alternative-id":["10.1145\/1277548.1277577","10.1145\/1277548"],"URL":"https:\/\/doi.org\/10.1145\/1277548.1277577","relation":{},"subject":[],"published":{"date-parts":[[2007,7,29]]},"assertion":[{"value":"2007-07-29","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}