Worst case tractability of linear problems in the presence of noise: linear information

IF 2.2 4区数学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of complex networks Pub Date : 2023-03-29 DOI:10.48550/arXiv.2303.16328

L. Plaskota, Pawe l Siedlecki

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.

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存在噪声的线性问题的最坏情况可跟踪性:线性信息

研究了定义在可分离希尔伯特空间上的多元线性问题的最坏情况可跟踪性。关于问题实例的信息由任意有界线性泛函的噪声评估组成，其中噪声要么是确定性的，要么是随机的。单次求值的代价取决于它的精度，并由代价函数控制。我们建立了具有噪声信息的问题的可跟踪性、成本函数和具有精确信息的相同问题的可跟踪性之间的相互作用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of complex networks MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

4.20

自引率

9.50%

发文量

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