论文标题
关于非架构的布罗德登方法
On a non-archimedean broyden method
论文作者
论文摘要
牛顿的方法是在Archimedean和非Archimedean设置中求解方程式的无处不在工具 - 它并没有真正差异。布罗登（Broyden）是所谓的“准牛顿方法”的煽动者。这些方法使用迭代步骤，其中不需要计算完整的雅各布矩阵或逆向。我们在一般的非Archimedean环境中提供了Broyden方法的适应，与缺乏内部产品兼容，并研究其Q和R收敛。我们证明，我们的改编方法至少将Q线性和r-superlinearearialearialearly与R-order $ 2^{\ frac {1} {2m}} $在dimension m中收敛。提供了数值数据。
Newton's method is an ubiquitous tool to solve equations, both in the archimedean and non-archimedean settings -- for which it does not really differ. Broyden was the instigator of what is called "quasi-Newton methods". These methods use an iteration step where one does not need to compute a complete Jacobian matrix nor its inverse. We provide an adaptation of Broyden's method in a general non-archimedean setting, compatible with the lack of inner product, and study its Q and R convergence. We prove that our adapted method converges at least Q-linearly and R-superlinearly with R-order $2^{\frac{1}{2m}}$ in dimension m. Numerical data are provided.
