ABSTRACT This article describes a new algorithm for generating correlation matrices with specified eigenvalues. The algorithm uses the method of alternating projections (MAP) that was first described by Neumann. The MAP algorithm for generating correlation matrices is both easy to understand and to program in higher-level computer languages, making this method accessible to applied researchers with no formal training in advanced mathematics. Simulations indicate that the new algorithm has excellent convergence properties. Correlation matrices with specified eigenvalues can be profitably used in Monte Carlo research in statistics, psychometrics, computer science, and related disciplines. To encourage such use, R code (R Core Team) for implementing the algorithm is provided in the supplementary material.

中文翻译：

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使用交替投影的方法生成具有指定特征值的相关矩阵

摘要 本文描述了一种用于生成具有指定特征值的相关矩阵的新算法。该算法使用由 Neumann 首次描述的交替投影 (MAP) 方法。用于生成相关矩阵的 MAP 算法既易于理解，又易于使用高级计算机语言进行编程，这使得没有接受过高级数学正规培训的应用研究人员可以使用这种方法。仿真表明新算法具有优良的收敛性。具有指定特征值的相关矩阵可用于统计、心理测量学、计算机科学和相关学科的蒙特卡罗研究。为了鼓励这种使用，补充材料中提供了用于实现算法的 R 代码（R 核心团队）。