GENERATION OF RANDOM ORTHOGONAL MATRICES
GENERATION OF RANDOM ORTHOGONAL MATRICES
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DOI：
10.1137/0908055
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发表时间：
1987-07-01
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影响因子：
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通讯作者：
UNDERHILL, LG
中科院分区：
文献类型：
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作者：
ANDERSON, TW;OLKIN, I;UNDERHILL, LG
为了生成根据正交群上的 Haar 测度分布的随机正交矩阵，很自然地从正态随机变量矩阵开始，然后通过奇异值分解将其分解。通过使用 Householder 变换可以获得更有效的方法。我们提出了另一种基于正交矩阵乘积的替代方案，每个正交矩阵代表一个旋转角度。对替代方法进行了一些数值比较。
In order to generate a random orthogonal matrix distributed according to Haar measure over the orthogonal group it is natural to start with a matrix of normal random variables and then factor it by the singular value decomposition. A more efficient method is obtained by using Householder transformations. We propose another alternative based on the product oforthogonal matrices, each of which represents an angle of rotation. Some numerical comparisons of alternative methods are made.