p-adic QR算法的超线性收敛
Super-linear convergence in the p-adic QR-algorithm
摘要：
QR算法是线性代数中最重要的算法之一。它的几个变体使得计算数值实矩阵或复矩阵的特征值和特征向量成为可能，即使矩阵的维数很大。第一作者于2019年首次将QR算法应用于局部域。然而，在该版本中，收敛的收敛速率仅是线性的，并且在某些情况下，分解成不变子空间是不完整的。我们提出了一种改进的算法，在许多情况下具有超线性收敛速率。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
