球上最小二乘问题向后误差的估计

An Estimation of the Backward Error for the LSS Problem Over a Sphere

A.N.Malyshev给出了球上最小二乘问题计算解的最佳向后扰动量表达式。从该表达式出发计算最佳向后扰动量却是很困难的。本文给出 1种有效的估算方法 ,所得结果对检验计算解的向后稳定性是有用的。并用几个简单的数值例子验证了所给算法的有效性。

an eleglant expression of the optimal backward perturbation bound for the problem of least squares over a sphere was presented by Malyshev. However,it seems to be difficult to compute such a bound. In this paper, an estimation of this bound which can be easily computed is given and the results obtained are of use for the check of the backward stability of computation. The results are illustrated by several simple numerical examples.