求解等式约束不定最小二乘校正问题的一种数值方法

A Numerical Algorithm for the Equality Constrained Indefinite Updating Least Squares Problems

主要考虑求解等式约束不定最小二乘校正问题。基于不定对称矩阵的反三角矩阵分解,给出了求解不定最小二乘更新问题的一种数值方法。该算法主要通过正交相似变换将对应的增广矩阵化为块下反三角形式,使得原线性系统变得更易于求解,同时也给出了原问题和校正问题的解之间的关系。数值实验表明本文给出的数值方法是有效的,可以得到较精确的近似解。

In this paper,we mainly consider the problem of solving equality constrained indefinite least squares.Based on the anti-triangular factorization of indefinite symmetric matrix,a numerical method is presented to solve the updating indefinite least squares problem.The corresponding augmented matrix is transformed to anti-triangular form using the orthogonal similarity transformations,and then the original linear system becomes easier to solve.We also give the relationships of the original least squares problem and updating least squares problem.Numerical experiments show that the numerical method is effective and can obtain more accurate approximate solutions.