标题： 预处理双共轭梯度算法中的多项式结构与预处理系统的切换方向 显示英文标题

标题： Structure of the polynomials in preconditioned BiCG algorithms and the switching direction of preconditioned systems

摘要： 我们提出一个定理，定义双共轭梯度（BiCG）方法的预处理系统的方向，并将其扩展到预处理的双Lanczos型算法。我们表明，预处理系统的方向通过构造和初始影子残量向量的设置而切换。我们分析并比较了四种预处理BiCG算法的多项式结构。 显示英文摘要

摘要： We present a theorem that defines the direction of a preconditioned system for the bi-conjugate gradient (BiCG) method, and we extend it to preconditioned bi-Lanczos-type algorithms. We show that the direction of a preconditioned system is switched by construction and by the settings of the initial shadow residual vector. We analyze and compare the polynomial structures of four preconditioned BiCG algorithms.