用Givens变换解最小二乘问题

Solving the Least Squares Problem with Givens Transformation

Givens变换提供一个不通过组成法方程解最小二乘问题的途径。这种解法具有数值稳定性好、计算效率高和节省内存等优点,它也适用于序贯平差。文中首先介绍了Givens变换的概念,叙述了用Givens变换解最小二乘问题的计算步骤,最后提供了更新未知参数及其协方差矩阵的算法。作为附录,给出了法方程矩阵的三角分解,以补充说明设计矩阵的Givens变换结果。

Givens transformation provides an approach to solving the least squares problem without forming normal equations. This approach is advantageous in terms of numerical stability, computational efficiency and storage saving. It is also suitable for sequential adjustment. This paper will first give the concept of Givens transformation, and then describe the computational procedure of solving the least squares prob-lim using Givens transformation, and finally deal with the algorithm of updating the parameter solutions and their covariance matrix. The triangular decomposition of normal equation matrix is appended supplementarily explaining the outcome of Givens transformation of a design matrix.