Stabilized hyperbolic Householder transformations
Stabilized hyperbolic Householder transformations
复制标题
DOI：
10.1109/icassp.1989.266669
复制
发表时间：
1989-05
期刊：
影响因子：
--
通讯作者：
A. Bojanczyk;A. Steinhardt
中科院分区：
文献类型：
--
作者：
A. Bojanczyk;A. Steinhardt
作者介绍了双曲Householder格式的修改，该格式在理论上是稳定的（根据已建立的稳定性准则），并在模拟中表现出上级数值行为。修改后的变换方案的影响，通过应用传统的正交，而不是双曲线，Householder变换的数据的Cholesky因素的降级。后者具有更好的数值特性。然而，这些标准正交算子本身的建设需要双曲计算。因此，该方法在某种意义上是半双曲半正交的。这些稳定的双曲Householder变换没有计算损失，它们的运算次数与常规变换相同。这种方法提供了大约两倍的节省方案的基础上的多个应用程序的单一向量downdating方案，它是一样稳定。
The authors introduce a modification of the hyperbolic Householder scheme that is demonstrably stable theoretically (according to an established stability criterion) and exhibits superior numerical behavior in simulations. The modified transform scheme effects downdating of Cholesky factors by applying conventional orthonormal, rather than hyperbolic, Householder transformations to the data. The latter have preferable numerical properties. However, the construction of these orthonormal operators itself requires hyperbolic computations. Thus the method is, in some sense, half hyperbolic and half orthonormal. There is no computational penalty incurred with these stabilized hyperbolic Householder transforms; they enjoy an operation count identical to that of their conventional counterparts. This approach offers roughly a twofold saving over schemes based on the multiple application of single vector downdating schemes, and it is just as stable.>