关于用Broyden方法解线性方程组终止性的讨论

A Note on Termination of Broyden Method for Linear System of Equations

D．P．O’Leary在一定条件下证明了Broyden方法在求解n维线性方程组时至多2n步终止，又指出当该条件不成立时终止将提前发生。本文中对后者证明了既存在着提前终止的情况，也存在着恰好2n步终止的情况。

D. P. O'Leary has proved that Broyden method must terminate in at most 2n steps on linear system of equations with n variables under certain conditions. He said that the termination would actually occur earlier when the conditions do not hold. It is proved that the Broyden method can be terminated earlier and/or terminated in 2n steps exactly when the conditions do not hold.