Christoffel–Darboux核是近似理论中的核心对象，在现代数据分析中有许多潜在的用途，包括在机器学习中的应用。这是第一本快速介绍这一主题的书，展示了一个简单工具的惊人效果。为了弥合经典数学和当前进化研究之间的鸿沟，作者详细介绍了这个主题，并采用了一种启发式的、基于实例的方法，假设只具备函数分析、概率和代数几何的一些基本概念的基本背景。它们涵盖了纯数学和应用数学的新成果，并介绍了对现代定量和定性科学具有广泛潜在影响的技术。综合笔记提供历史背景，讨论高级概念，并提供详细的参考书目。数学、统计学、工程或经济学领域的研究人员和研究生将发现传统主题的新视角，以及具有挑战性的开放性问题。
The Christoffel–Darboux Kernel for Data Analysis
The Christoffel–Darboux kernel, a central object in approximation theory, is shown to have many potential uses in modern data analysis, including applications in machine learning. This is the first book to offer a rapid introduction to the subject, illustrating the surprising effectiveness of a simple tool. Bridging the gap between classical mathematics and current evolving research, the authors present the topic in detail and follow a heuristic, example-based approach, assuming only a basic background in functional analysis, probability and some elementary notions of algebraic geometry. They cover new results in both pure and applied mathematics and introduce techniques that have a wide range of potential impacts on modern quantitative and qualitative science. Comprehensive notes provide historical background, discuss advanced concepts and give detailed bibliographical references. Researchers and graduate students in mathematics, statistics, engineering or economics will find new perspectives on traditional themes, along with challenging open problems.
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