Developments of new linear solvers based on the induced dimension reduction theorem

Krylov子空间方法，特别是混合BiCG方法是在20世纪90年代发展起来的，混合BiCG方法的一些优点是众所周知的。S在2007年提出了一种新的方法，称为诱导降维(简称IDR)。最近有报道称，IDR(S)方法有时比混合的BiCG方法收敛得更快。S(IDR)方法已成为众多研究者关注的焦点。因此，我们结合了IDR(S)和混合BiCG方法的优点，提出了比混合BiCG方法和原始IDR(S)方法具有更好的收敛性能的新的求解器。

Krylov subspace methods, specifically hybrid Bi-CG methods, have been developed in the 1990s, and some advantages with the hybrid BiCG methods are well-known. A new method which is called the Induced Dimension Reduction (abbreviated to IDR) (s) has been proposed in 2007. It has recently reported that the IDR(s) method sometimes converges faster than the hybrid Bi-CG methods. Many researchers have focused on the IDR(s) method. Therefore, by combining the advantage of IDR(s) with that of the hybrid Bi-CG methods, we have proposed new solvers which have better convergence than the hybrid Bi-CG and original IDR(s) methods.