吉文斯变换及其在序贯最小二乘平差中的应用

利用吉文斯变换解最小二乘问题,具有无须组成法方程,有良好的数值稳定性,利于利用矩阵的稀疏性,尤其便于各类序贯平差等优点。本文着重论述该变换在序贯最小二乘平差中的应用。

Givens Transformations and Its Application to Sequential Least-squares Adjustment

For on-line system it is necessary to introduce seqential algorithm matching mith dynamic collection and on -line editing of the data. Using Givens Transformations to solve linear least-squares problems allows to process an overde-termined leaner system of equations row by row directly into an inconsistent upper triangular system without forming normal equations. It is in particular convenient to seqential updating of the data and exploiting original sparsity of design matrix. In this paper the principle of Givens Transformations is described, and its performance in sequential least-squares adjustment is especially emphasized.