{"title":"通过观测具有线性湍流扰动的解来识别差分方程","authors":"A. A. Lomov","doi":"10.1134/s1055134424030064","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study the Prony identification problem for coefficients of an autonomous difference\nequation by observations of noisy solutions with unknown additive perturbations from an arbitrary\nlinear manifold. We establish a “projectivity” property of the variational objective function. For\ntwo main types of equations, we obtain criteria and sufficient conditions for identifiability.\n</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Identification of Difference Equations by Observations of Solutions with Perturbations from a Linear Manifold\",\"authors\":\"A. A. Lomov\",\"doi\":\"10.1134/s1055134424030064\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p> We study the Prony identification problem for coefficients of an autonomous difference\\nequation by observations of noisy solutions with unknown additive perturbations from an arbitrary\\nlinear manifold. We establish a “projectivity” property of the variational objective function. For\\ntwo main types of equations, we obtain criteria and sufficient conditions for identifiability.\\n</p>\",\"PeriodicalId\":39997,\"journal\":{\"name\":\"Siberian Advances in Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Siberian Advances in Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1134/s1055134424030064\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Siberian Advances in Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1055134424030064","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Identification of Difference Equations by Observations of Solutions with Perturbations from a Linear Manifold
Abstract
We study the Prony identification problem for coefficients of an autonomous difference
equation by observations of noisy solutions with unknown additive perturbations from an arbitrary
linear manifold. We establish a “projectivity” property of the variational objective function. For
two main types of equations, we obtain criteria and sufficient conditions for identifiability.
期刊介绍：
Siberian Advances in Mathematics is a journal that publishes articles on fundamental and applied mathematics. It covers a broad spectrum of subjects: algebra and logic, real and complex analysis, functional analysis, differential equations, mathematical physics, geometry and topology, probability and mathematical statistics, mathematical cybernetics, mathematical economics, mathematical problems of geophysics and tomography, numerical methods, and optimization theory.
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