Selected aspects of tractability analysis

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2024-05-31 DOI:10.1016/j.jco.2024.101869

Peter Kritzer

引用次数: 0

Abstract

We give an overview of certain aspects of tractability analysis of multivariate problems. This paper is not intended to give a complete account of the subject, but provides an insight into how the theory works for particular types of problems. We mainly focus on linear problems on Hilbert spaces, and mostly allow arbitrary linear information. In such cases, tractability analysis is closely linked to an analysis of the singular values of the operator under consideration. We also highlight the more recent developments regarding exponential and generalized tractability. The theoretical results are illustrated by several examples throughout the article.

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可操作性分析的若干方面

我们概述了多元问题可操作性分析的某些方面。本文并不打算对这一主题进行完整的阐述，而是想让大家了解这一理论是如何在特定类型的问题中发挥作用的。我们主要关注希尔伯特空间上的线性问题，而且大多允许任意线性信息。在这种情况下，可操作性分析与所考虑的算子奇异值分析密切相关。我们还强调了有关指数可控性和广义可控性的最新进展。文章通篇通过几个例子对理论结果进行了说明。

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.