Research on GBi-CGSTAB, a new solver for large scale linear systems

在GBi-CGSTAB（一种新的大规模线性系统求解器）上获得了以下结果：GBi-CGSTAB具有残差自动校正功能，可避免伪收敛，新发现“残差与真残差之差在迭代初期保持不变”，GBi-CGSTAB与IDRSTAB的比较，GBi-CGSTAB对移位线性系统的应用，GBi-CGSTAB的简明推导，BiO-ML（s）BiCG：与GBi-CGSTAB相关的新求解器。

The following results have been obtained on GBi-CGSTAB, a new solver for large scale linear systems: GBi-CGSTAB equipped with auto-correction of residuals to avoid spurious convergence, a new findings ‘the difference between the residual and the true residual remains constant from the early stage on the iteration’, comparison between GBi-CGSTAB and IDRSTAB, GBi-CGSTAB for shifted linear systems, concise derivation of GBi-CGSTAB， BiO-ML(s)BiCG: a new solver related to GBi-CGSTAB.