Computational Techniques for Real Logarithms of Matrices
Computational Techniques for Real Logarithms of Matrices
复制标题
矩阵实对数的计算技术
DOI：
10.1137/s0895479894273614
复制
发表时间：
1996
期刊：
影响因子：
--
通讯作者：
A. Papini
中科院分区：
文献类型：
--
作者：
L. Dieci;B. Morini;A. Papini
在这项工作中，我们考虑计算实矩阵的实对数。我们关注一般的条件问题，提供了包括缩放问题在内的几种技术的仔细实现，最后在一些问题上测试和比较了这些技术。考虑到所有的事情，我们推荐的通用方法是带有特征值分组的舒尔分解方法，其次是对角线块的平方根和对角线块的对角线近似。尽管如此，在某些情况下，实现良好的级数展开技术优于其他方法。我们还分析并实现了一种新的估计$\log$的法氏导数的方法，该方法在条件估计中非常成功。
In this work, we consider computing the real logarithm of a real matrix. We pay attention to general conditioning issues, provide careful implementation for several techniques including scaling issues, and finally test and compare the techniques on a number of problems. All things considered, our recommendation for a general purpose method goes to the Schur decomposition approach with eigenvalue grouping, followed by square roots and diagonal Padé approximants of the diagonal blocks. Nonetheless, in some cases, a well-implemented series expansion technique outperformed the other methods. We have also analyzed and implemented a novel method to estimate the Frechét derivative of the $\log$, which proved very successful for condition estimation.