解最小二乘问题的一种混合方法的误差分析

An error analysis of a hybrid method for the least squares problem

对于线性最小二乘问题 ,混合方法的提出是企图在法方程法与 QR分解方法之间取得某种平衡 ,希望能够节省计算量又同时保持计算解达到较高精度 ,但后者在理论上并未得到证明 .经对混合方法的详细误差分析 ,证明了这种混合方法不一定能得到比法方程法精度更高的计算解 ,甚至可能要差 .因混合方法的计算量高于法方程法 ,所以该方法并未达到理想的要求 ,不一定是好的选择 .

For the LS problem, the method of normal equations needs less computation but its computed solution has poor accuracy. If QR factorization is used, more accurate solution can be got. However, its computation is nearly as twice as the method of normal equations. To take advantage of the merits of these two methods, a hybrid method has been proposed to keep cheap computation without degenerating the accuracy of the solution too much. This paper proves that, the hybrid method can not obtain more accurate solution than the method of normal equations, so it does not achieve the desired goal and may not be a good method.