Hyperbolic householder transformations, definition and application

A class of transformation matrices, analogous to the Householder matrices, is developed with a non-orthogonal 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 exists 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, but if a relatively small fraction of the data set is modified, there is a reduction in required computations.