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

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2023-07-26 DOI:10.1016/j.jco.2023.101782

Leszek Plaskota, Paweł 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 Complexity 工程技术-计算机：理论方法

CiteScore

3.10

自引率

17.60%

发文量

审稿时长

>12 weeks

期刊介绍： The multidisciplinary Journal of Complexity publishes original research papers that contain substantial mathematical results on complexity as broadly conceived. Outstanding review papers will also be published. In the area of computational complexity, the focus is on complexity over the reals, with the emphasis on lower bounds and optimal algorithms. The Journal of Complexity also publishes articles that provide major new algorithms or make important progress on upper bounds. Other models of computation, such as the Turing machine model, are also of interest. Computational complexity results in a wide variety of areas are solicited. Areas Include: • Approximation theory • Biomedical computing • Compressed computing and sensing • Computational finance • Computational number theory • Computational stochastics • Control theory • Cryptography • Design of experiments • Differential equations • Discrete problems • Distributed and parallel computation • High and infinite-dimensional problems • Information-based complexity • Inverse and ill-posed problems • Machine learning • Markov chain Monte Carlo • Monte Carlo and quasi-Monte Carlo • Multivariate integration and approximation • Noisy data • Nonlinear and algebraic equations • Numerical analysis • Operator equations • Optimization • Quantum computing • Scientific computation • Tractability of multivariate problems • Vision and image understanding.