On the Global Convergence of Broyden''s Method
On the Global Convergence of Broyden''s Method
复制标题
DOI：
10.1090/s0025-5718-1976-0418451-2
复制
发表时间：
1974-10
影响因子：
2
通讯作者：
J. J. Moré-J.;J. Trangenstein
中科院分区：
文献类型：
--
作者：
J. J. Moré-J.;J. Trangenstein
我们考虑求解非线性方程的Broyden‘’S 1965方法。如果映射是线性的，则该方法的简单修改就能保证全局收敛和q-超线性收敛。对于非线性映射，证明了由Powell提出的求解非线性方程的混合策略在搜索方向为一致线性独立序列的情况下会导致R-超线性收敛。然后我们讨论了最后一个概念及其与Broyden‘’S方法的联系。最后，我们指出上述结果如何推广到Powell‘’S对称形式的Broyden‘S方法。
We consider Broyden''s 1965 method for solving nonlinear equations. If the mapping is linear, then a simple modification of this method guarantees global and Q-superlinear convergence. For nonlinear mappings it is shown that the hybrid strategy for nonlinear equations due to Powell leads to R-superlinear convergence provided the search directions from a uniformly linearly indepenent sequence. We then explore this last concept and its connection with Broyden''s method. Finally, we point out how the above results extend to Powell''s symmetric version of Broyden''s method.