论文标题
对随机正交和统一矩阵的特征值取样
Sampling the eigenvalues of random orthogonal and unitary matrices
论文作者
论文摘要
我们开发了一种有效的算法，用于对正交或统一组的HAAR度量分布的随机矩阵进行采样。我们的技术直接示例了此类矩阵的Hessenberg形式的分解，然后使用定制的核心座算法计算其特征值。这种方法需要许多在采样的矩阵顺序上是二次的浮点操作，并且可以适应其他矩阵组。特别是，我们解释了如何使用特殊的正交和单一组对HAAR度量进行采样，以及通过要求采样矩阵的决定因素在复杂单位圆上获得给定的复数数字，从而获得了条件概率分布。
We develop an efficient algorithm for sampling the eigenvalues of random matrices distributed according to the Haar measure over the orthogonal or unitary group. Our technique samples directly a factorization of the Hessenberg form of such matrices, and then computes their eigenvalues with a tailored core-chasing algorithm. This approach requires a number of floating-point operations that is quadratic in the order of the matrix being sampled, and can be adapted to other matrix groups. In particular, we explain how it can be used to sample the Haar measure over the special orthogonal and unitary groups and the conditional probability distribution obtained by requiring the determinant of the sampled matrix be a given complex number on the complex unit circle.
