中文摘要：

我们建议一个二次的联盟者为计算一个 Hermitian 矩阵的不变的潜水艇空格的会聚的算法。算法的每次重复由一矩阵矩阵增加和一 QR 分解组成。我们在场没有使用大 O 符号的算法的精确集中分析。我们也基于允许我们与几存在算法做连接并且与更快的集中率导出对我们的基本算法的扩展的类的含蓄的合理转变建议一个一般框架。几个数字例子被给它比较存在算法和新算法的一些方面。

英文摘要：

We propose a quadratically convergent algorithm for computing the invariant subspaces of an Hermitian matrix. Each iteration of the algorithm consists of one matrix-matrix multiplication and one QR decomposition. We present an accurate convergence analysis of the algorithm without using the big O notation. We also propose a general framework based on implicit rational transformations which allows us to make connections with several existing algorithms and to derive classes of extensions to our basic algorithm with faster convergence rates. Several numerical examples are given which compare some aspects of the existing algorithms and the new algorithms.