We study approximation of the embedding $\ell_p^m \rightarrow \ell_{\infty}^m$, $1 \leq p \leq 2$, based on randomized adaptive algorithms that use arbitrary linear functionals as information on a problem instance. We show upper bounds for which the complexity $n$ exhibits only a $(\log\log m)$-dependence. Our results for $p=1$ lead to an example of a gap of order $n$ (up to logarithmic factors) for the error between best adaptive and non-adaptive Monte Carlo methods. This is the largest possible gap for linear problems.
Enhanced randomized Douglas-Rachford method for linear systems: Improved probabilities and adaptive momentum
School of Mathematical Sciences, Beihang University（北京航空航天大学数学科学学院）；LMIB of the Ministry of Education, School of Mathematical Sciences, Beihang University（教育部重点实验室，北京航空航天大学数学科学学院）
Adaptive Randomized Extended Bregman-Kaczmarz Method for Combined Optimization Problems
Shanghai Research Institute for Intelligent Autonomous Systems, Tongji University（同济大学上海智能自主系统研究院）；School of Mathematical Sciences, Tongji University（同济大学数学科学学院）；The Institute for Advanced Study, Shenzhen University（深圳大学高等研究院）
Adaptive-Growth Randomized Neural Networks for PDEs: Algorithms and Numerical Analysis
School of Mathematics and Statistics, Xi’an Jiaotong University（西安交通大学数学与统计学院）；School of Mathematics and Statistics & State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University（西安交通大学数学与统计学院及动力工程多相流国家重点实验室）；Institute of Applied Physics and Computational Mathematics（应用物理与计算数学研究所）
Adaptive Randomized Tensor Train Rounding using Khatri-Rao Products
Scientific Computing Department, STFC（STFC 科学计算部）；Rutherford Appleton Laboratory（鲁瑟福·阿普尔顿实验室）；Department of Computer Science, Wake Forest University（维克森林大学计算机科学系）；Institute of Mathematics, EPFL（洛桑联邦理工学院数学研究所）；PSI Center for Scientific Computing, Theory and Data（瑞士保罗谢勒研究所科学计算、理论与数据中心）；Department of Mathematics, North Carolina State University（北卡罗来纳州立大学数学系）
Precision-induced Adaptive Randomized Low-Rank Approximation for SVD and Matrix Inversion
Nanjing University of Information Science and Technology（南京信息工程大学）；Xi’an Jiaotong University（西安交通大学）；Xiamen University（厦门大学）；Pengcheng Laboratory（鹏城实验室）
Matrix-free construction of HSS representation using adaptive randomized sampling
University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；University of Manchester（曼彻斯特大学）；Livermore Software Technology Corporation（利弗莫尔软件技术公司）
Adaptive-Growth Randomized Neural Networks for Level-Set Computation of Multivalued Nonlinear First-Order PDEs with Hyperbolic Characteristics
School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China（数学与统计学学院，西安交通大学，西安，陕西 710049，中国）；School of Mathematical Sciences & Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China（数学科学学院及自然科学研究所，上海交通大学，上海 200240，中国）；School of Mathematics and Statistics & State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China（数学与统计学学院及电力工程多相流国家重点实验室，西安交通大学，西安，陕西 710049，中国）
Adaptive Randomized Neural Networks for PDEs: Structure-Aware Feature Redistribution and Residual-Driven Block Enrichment
School of Mathematics and Statistics, Xi’an Jiaotong University（西安交通大学数学与统计学院）；School of Mathematics and Statistics & State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University（西安交通大学数学与统计学院）
Constrained Optimization via Exact Augmented Lagrangian and Randomized Iterative Sketching
University of Chicago（芝加哥大学）；University of California, Berkeley（加州大学伯克利分校）；International Computer Science Institute（国际计算机科学研究所）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
IterativeCUR: Large Rank-Adaptive Approximation From a Small Recycled Sketch
Mathematical Institute at the University of Oxford（牛津大学数学研究所）；Institute of Mathematics at EPFL（洛桑联邦理工学院数学研究所）；Department of Mathematics and the Oden Institute at the University of Texas at Austin（德克萨斯大学奥斯汀分校数学系与奥登学院）
