Probabilistic Upper Bounds for the Matrix Two-Norm
Probabilistic Upper Bounds for the Matrix Two-Norm
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DOI：
10.1007/s10915-013-9716-x
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发表时间：
2013-04
影响因子：
2.5
通讯作者：
M. Hochstenbach
中科院分区：
文献类型：
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作者：
M. Hochstenbach
我们开发了矩阵二范数的概率上限，即最大奇异值。这些界限是用户选择的高概率的真实上限，是通过 Lanczos 双对角化过程中隐含出现的许多不同多项式导出的。由于这些多项式是自适应生成的，因此边界通常会给出非常好的结果。它们可以被有效地计算。与保证下界的近似值一起，这可能会导致大矩阵的矩阵范数在几分之一秒内出现较小的概率区间。
We develop probabilistic upper bounds for the matrix two-norm, the largest singular value. These bounds, which are true upper bounds with a user-chosen high probability, are derived with a number of different polynomials that implicitly arise in the Lanczos bidiagonalization process. Since these polynomials are adaptively generated, the bounds typically give very good results. They can be computed efficiently. Together with an approximation that is a guaranteed lower bound, this may result in a small probabilistic interval for the matrix norm of large matrices within a fraction of a second.