Lanczos方法用于解大型稀疏复线性方程组的几个问题

Some problems in using Lanczos method to solve large sparse complex linear systems

给出并证明了HermitianLanczos算法理论基础的定理；讨论了解大型稀疏复线性方程组的Lancsos方法与复双共轭梯度法（CBCG法）的等价性；证明了应用于复对称线性方程组时的一个重要关系式。

As theoretical basis of Hermitian Lanczos algorithm, two theorems are proved at first, then the equivalence between Lanczos method and the complex biconjugate gradient method (CBCG method) for solving large sparse complex linear systems is discussed, an important relationship for the complex symmetric case is also proved.