This paper introduces fast R updating algorithms specifically designed for statistical applications, including regression, filtering, and model selection, where data structures change frequently. Although traditional QR decomposition is essential for matrix operations, it becomes computationally intensive when dynamically updating the design matrix in statistical models. The proposed algorithms efficiently update the R matrix without the need for recalculation of Q, thereby significantly reducing computational costs in practical computational scenarios. The provision of scalable solutions for high-dimensional regression models is a key strength of these algorithms, enhancing the feasibility of large-scale statistical analyses and model selection in data-intensive fields. A thorough simulation study and the analysis of real-world data demonstrate that the methods achieve a substantial reduction in computational time without compromising accuracy. The discussion illustrates the benefits of these algorithms across a wide range of models and applications in statistics and machine learning.

翻译：本文介绍了专门为统计应用设计的快速R矩阵更新算法，涵盖回归、滤波和模型选择等数据结构频繁变化的场景。尽管传统的QR分解在矩阵运算中至关重要，但在统计模型中动态更新设计矩阵时，其计算负担显著增加。所提出的算法能够高效更新R矩阵而无需重新计算Q矩阵，从而在实际计算场景中大幅降低计算成本。这些算法的核心优势在于为高维回归模型提供可扩展的解决方案，提升了数据密集型领域中进行大规模统计分析和模型选择的可行性。通过详尽的模拟研究和实际数据分析表明，这些方法在保证精度的同时实现了计算时间的显著降低。讨论部分阐明了这些算法在统计学与机器学习各类模型和应用中的广泛效益。