{"title":"Worst case tractability of linear problems in the presence of noise: linear information","authors":"L. Plaskota, Pawe l Siedlecki","doi":"10.48550/arXiv.2303.16328","DOIUrl":null,"url":null,"abstract":"We study the worst case tractability of multivariate linear problems defined on separable Hilbert spaces. Information about a problem instance consists of noisy evaluations of arbitrary bounded linear functionals, where the noise is either deterministic or random. The cost of a single evaluation depends on its precision and is controlled by a cost function. We establish mutual interactions between tractability of a problem with noisy information, the cost function, and tractability of the same problem, but with exact information.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":"298 1","pages":"101782"},"PeriodicalIF":2.2000,"publicationDate":"2023-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of complex networks","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.48550/arXiv.2303.16328","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
We study the worst case tractability of multivariate linear problems defined on separable Hilbert spaces. Information about a problem instance consists of noisy evaluations of arbitrary bounded linear functionals, where the noise is either deterministic or random. The cost of a single evaluation depends on its precision and is controlled by a cost function. We establish mutual interactions between tractability of a problem with noisy information, the cost function, and tractability of the same problem, but with exact information.
期刊介绍：
Journal of Complex Networks publishes original articles and reviews with a significant contribution to the analysis and understanding of complex networks and its applications in diverse fields. Complex networks are loosely defined as networks with nontrivial topology and dynamics, which appear as the skeletons of complex systems in the real-world. The journal covers everything from the basic mathematical, physical and computational principles needed for studying complex networks to their applications leading to predictive models in molecular, biological, ecological, informational, engineering, social, technological and other systems. It includes, but is not limited to, the following topics: - Mathematical and numerical analysis of networks - Network theory and computer sciences - Structural analysis of networks - Dynamics on networks - Physical models on networks - Networks and epidemiology - Social, socio-economic and political networks - Ecological networks - Technological and infrastructural networks - Brain and tissue networks - Biological and molecular networks - Spatial networks - Techno-social networks i.e. online social networks, social networking sites, social media - Other applications of networks - Evolving networks - Multilayer networks - Game theory on networks - Biomedicine related networks - Animal social networks - Climate networks - Cognitive, language and informational network
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