论文标题
P-ADIC QR-ALGORITHM中的超线性收敛
Super-linear convergence in the p-adic QR-algorithm
论文作者
论文摘要
QR-Algorithm是线性代数中最重要的算法之一。它的几种变体使数值真实或复杂矩阵的特征值和特征向量的计算使其可行，即使矩阵的尺寸是巨大的。 QR-Algorithm对本地字段的首次改编是由第一作者在2019年给出的。但是，在此版本中，收敛速率仅是线性的，在某些情况下，将分解为不变子空间的分解是不完整的。在许多情况下，我们对该算法进行了超级线性收敛速率的改进。
The QR-algorithm is one of the most important algorithms in linear algebra. Its several variants make feasible the computation of the eigenvalues and eigenvectors of a numerical real or complex matrix, even when the dimensions of the matrix are enormous. The first adaptation of the QR-algorithm to local fields was given by the first author in 2019. However, in this version the rate of convergence is only linear and in some cases the decomposition into invariant subspaces is incomplete. We present a refinement of this algorithm with a super-linear convergence rate in many cases.
