{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:08:44Z","timestamp":1750306124710,"version":"3.41.0"},"reference-count":3,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2017,5,18]],"date-time":"2017-05-18T00:00:00Z","timestamp":1495065600000},"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":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2017,5,18]]},"abstract":"<jats:p>\n            We consider the problem of sparse interpolation of a multivariate black-box polynomial in floatingpoint arithmetic. More specifically, we assume that we are given a black-box polynomial\n            <jats:italic>f<\/jats:italic>\n            (\n            <jats:italic>x<\/jats:italic>\n            <jats:sub>1<\/jats:sub>\n            ,...\n            <jats:italic>x<\/jats:italic>\n            <jats:sub>n<\/jats:sub>\n            ) = \u03a3\n            <jats:sup>\n              <jats:italic>t<\/jats:italic>\n            <\/jats:sup>\n            <jats:sub>\n              <jats:italic>j<\/jats:italic>\n              =1\n            <\/jats:sub>\n            <jats:italic>c<\/jats:italic>\n            <jats:sub>\n              <jats:italic>j<\/jats:italic>\n            <\/jats:sub>\n            <jats:italic>x<\/jats:italic>\n            <jats:sub>1<\/jats:sub>\n            <jats:sup>\n              <jats:italic>d<\/jats:italic>\n              <jats:sub>\n                <jats:italic>j<\/jats:italic>\n                , 1\n              <\/jats:sub>\n            <\/jats:sup>\n            ...\n            <jats:italic>x<\/jats:italic>\n            <jats:sub>\n              <jats:italic>n<\/jats:italic>\n            <\/jats:sub>\n            <jats:sup>\n              <jats:italic>d<\/jats:italic>\n              <jats:sub>\n                <jats:italic>j<\/jats:italic>\n                , n\n              <\/jats:sub>\n            <\/jats:sup>\n            \u2208 C[\n            <jats:italic>x<\/jats:italic>\n            <jats:sub>1<\/jats:sub>\n            ,...,\n            <jats:italic>x<\/jats:italic>\n            <jats:sub>\n              <jats:italic>n<\/jats:italic>\n            <\/jats:sub>\n            ] (\n            <jats:italic>\n              c\n              <jats:sub>j<\/jats:sub>\n            <\/jats:italic>\n            \u2260 0)and the number of terms\n            <jats:italic>t<\/jats:italic>\n            , and that we can evaluate the value of\n            <jats:italic>f<\/jats:italic>\n            (\n            <jats:italic>\n              x\n              <jats:sup>1<\/jats:sup>\n              ,...,x\n              <jats:sub>n<\/jats:sub>\n              )\n            <\/jats:italic>\n            at any point in C\n            <jats:sup>\n              <jats:italic>n<\/jats:italic>\n            <\/jats:sup>\n            in floating-point arithmetic. The problem is to find the coefficients\n            <jats:italic>\n              c\n              <jats:sub>1<\/jats:sub>\n            <\/jats:italic>\n            , ...,\n            <jats:italic>\n              c\n              <jats:sub>t<\/jats:sub>\n            <\/jats:italic>\n            and the exponents\n            <jats:italic>\n              d\n              <jats:sub>1,1,<\/jats:sub>\n              ..., d\n              <jats:sub>t,n<\/jats:sub>\n            <\/jats:italic>\n            . We propose an efficient algorithm to solve the problem.\n          <\/jats:p>","DOI":"10.1145\/3096730.3096734","type":"journal-article","created":{"date-parts":[[2017,5,18]],"date-time":"2017-05-18T19:38:45Z","timestamp":1495136325000},"page":"18-20","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["An algorithm for symbolic-numeric sparse interpolation of multivariate polynomials whose degree bounds are unknown"],"prefix":"10.1145","volume":"51","author":[{"given":"Dai","family":"Numahata","sequence":"first","affiliation":[{"name":"Tokyo University of Science, Tokyo, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hiroshi","family":"Sekigawa","sequence":"additional","affiliation":[{"name":"Tokyo University of Science, Tokyo, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2017,5,18]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/62212.62241"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2008.09.002"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2008.11.003"}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3096730.3096734","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3096730.3096734","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T03:36:53Z","timestamp":1750217813000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3096730.3096734"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,5,18]]},"references-count":3,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,5,18]]}},"alternative-id":["10.1145\/3096730.3096734"],"URL":"https:\/\/doi.org\/10.1145\/3096730.3096734","relation":{},"ISSN":["1932-2240"],"issn-type":[{"type":"print","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2017,5,18]]},"assertion":[{"value":"2017-05-18","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}