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.