{"title":"高效反Z$变换和维纳-霍普夫因式分解","authors":"Svetlana Boyarchenko, Sergei Levendorskiĭ","doi":"arxiv-2404.19290","DOIUrl":null,"url":null,"abstract":"We suggest new closely related methods for numerical inversion of\n$Z$-transform and Wiener-Hopf factorization of functions on the unit circle,\nbased on sinh-deformations of the contours of integration, corresponding\nchanges of variables and the simplified trapezoid rule. As applications, we\nconsider evaluation of high moments of probability distributions and\nconstruction of causal filters. Programs in Matlab running on a Mac with\nmoderate characteristics achieves the precision E-14 in several dozen of\nmicroseconds and E-11 in several milliseconds, respectively.","PeriodicalId":501294,"journal":{"name":"arXiv - QuantFin - Computational Finance","volume":"14 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Efficient inverse $Z$-transform and Wiener-Hopf factorization\",\"authors\":\"Svetlana Boyarchenko, Sergei Levendorskiĭ\",\"doi\":\"arxiv-2404.19290\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We suggest new closely related methods for numerical inversion of\\n$Z$-transform and Wiener-Hopf factorization of functions on the unit circle,\\nbased on sinh-deformations of the contours of integration, corresponding\\nchanges of variables and the simplified trapezoid rule. As applications, we\\nconsider evaluation of high moments of probability distributions and\\nconstruction of causal filters. Programs in Matlab running on a Mac with\\nmoderate characteristics achieves the precision E-14 in several dozen of\\nmicroseconds and E-11 in several milliseconds, respectively.\",\"PeriodicalId\":501294,\"journal\":{\"name\":\"arXiv - QuantFin - Computational Finance\",\"volume\":\"14 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-04-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - QuantFin - Computational Finance\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2404.19290\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - QuantFin - Computational Finance","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2404.19290","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Efficient inverse $Z$-transform and Wiener-Hopf factorization
We suggest new closely related methods for numerical inversion of
$Z$-transform and Wiener-Hopf factorization of functions on the unit circle,
based on sinh-deformations of the contours of integration, corresponding
changes of variables and the simplified trapezoid rule. As applications, we
consider evaluation of high moments of probability distributions and
construction of causal filters. Programs in Matlab running on a Mac with
moderate characteristics achieves the precision E-14 in several dozen of
microseconds and E-11 in several milliseconds, respectively.
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