Hyperbolic householder transforms
Hyperbolic householder transforms
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DOI：
10.1137/0609022
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发表时间：
1988-04
影响因子：
1.5
通讯作者：
C. Rader;Allan O. Steinhard
中科院分区：
文献类型：
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作者：
C. Rader;Allan O. Steinhard
与 Householder 矩阵类似的一类变换矩阵是用非正交属性开发的，旨在允许从最小二乘问题中有效删除数据。这些矩阵（我们称之为双曲 Householder）被证明可以实现数据删除或同时添加和删除，而对舍入误差的敏感性比基于正态方程的技术要低得多。当添加/删除集很大时，这种数值鲁棒性是以计算量适度增加为代价获得的，而当仅修改数据集的相对一小部分时，所需计算量就会减少。考虑信号处理问题的两个应用。首先，这些变换用于获得用于加窗递归最小二乘滤波的平方根算法。其次，利用变换来实现自适应阵列中权重向量估计过程中的虚假数据的拒绝。
A class of transformation matrices, analogous to the Householder matrices, is developed with a nonorthogonal property designed to permit the efficient deletion of data from least-squares problems. These matrices, which we term hyperbolic Householder, are shown to effect deletion, or simultaneous addition and deletion, of data with much less sensitivity to rounding errors than for techniques based on normal equations. When the addition/deletion sets are large, this numerical robustness is obtained at the expense of only a modest increase in computations, and when only a relatively small fraction of the data set is modified, there is a decrease in required computations. Two applications to signal processing problems are considered. First, these transformations are used to obtain a square root algorithm for windowed recursive least-squares filtering. Second, the transformations are employed to implement the rejection of spurious data from the weight vector estimation process in an adaptive array.