{"title":"使用小素数的并行稀疏插值","authors":"Mohamed Khochtali, Daniel S. Roche, Xisen Tian","doi":"10.1145/2790282.2790290","DOIUrl":null,"url":null,"abstract":"To interpolate a supersparse polynomial with integer coefficients, two alternative approaches are the Prony-based \"big prime\" technique, which acts over a single large finite field, or the more recently-proposed \"small primes\" technique, which reduces the unknown sparse polynomial to many low-degree dense polynomials. While the latter technique has not yet reached the same theoretical efficiency as Prony-based methods, it has an obvious potential for parallelization. We present a heuristic \"small primes\" interpolation algorithm and report on a low-level C implementation using FLINT and MPI.","PeriodicalId":384227,"journal":{"name":"Proceedings of the 2015 International Workshop on Parallel Symbolic Computation","volume":"23 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Parallel sparse interpolation using small primes\",\"authors\":\"Mohamed Khochtali, Daniel S. Roche, Xisen Tian\",\"doi\":\"10.1145/2790282.2790290\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"To interpolate a supersparse polynomial with integer coefficients, two alternative approaches are the Prony-based \\\"big prime\\\" technique, which acts over a single large finite field, or the more recently-proposed \\\"small primes\\\" technique, which reduces the unknown sparse polynomial to many low-degree dense polynomials. While the latter technique has not yet reached the same theoretical efficiency as Prony-based methods, it has an obvious potential for parallelization. We present a heuristic \\\"small primes\\\" interpolation algorithm and report on a low-level C implementation using FLINT and MPI.\",\"PeriodicalId\":384227,\"journal\":{\"name\":\"Proceedings of the 2015 International Workshop on Parallel Symbolic Computation\",\"volume\":\"23 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-06-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 2015 International Workshop on Parallel Symbolic Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/2790282.2790290\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 2015 International Workshop on Parallel Symbolic Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2790282.2790290","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
To interpolate a supersparse polynomial with integer coefficients, two alternative approaches are the Prony-based "big prime" technique, which acts over a single large finite field, or the more recently-proposed "small primes" technique, which reduces the unknown sparse polynomial to many low-degree dense polynomials. While the latter technique has not yet reached the same theoretical efficiency as Prony-based methods, it has an obvious potential for parallelization. We present a heuristic "small primes" interpolation algorithm and report on a low-level C implementation using FLINT and MPI.