In this paper we introduce a new column selection strategy, named here ``Deviation Maximization", and apply it to compute rank-revealing QR factorizations as an alternative to the well known block version of the QR factorization with the column pivoting method, called QP3 and currently implemented in LAPACK's xgeqp3 routine. We show that the resulting algorithm, named QRDM, has similar rank-revealing properties of QP3 and better execution times. We present numerical test results on a wide data set of numerically singular matrices, which has become a reference in the recent literature.
翻译:在本文中,我们引入了一个新的列选择策略, 名为“ 降低最大化”, 并应用它来计算分级读取 QR 系数化, 以替代已知的 QR 系数化区块版本, 使用称为 QP3 的 QR 分队支线法, 并在 LAPACK 的 xgeqp3 常规中实施。 我们显示, 由此得出的算法, 名为 QRDM, 类似 QP3 的分级读取属性, 以及更好的执行时间 。 我们用一组数字单一矩阵的宽广数据来显示数字测试结果, 这些数据在最近文献中成为参考 。