论文标题
TRICG和TRIMR：对称准准系统的两种迭代方法
TriCG and TriMR: Two Iterative Methods for Symmetric Quasi-Definite Systems
论文作者
论文摘要
我们介绍了基于桑德斯（Saunders），Simon和Yip在1988年提出的正交的三角形成过程来求解Tricg和Trimr的迭代方法。我们评估了TRICG和TRIMR的性能在套件矩阵集合以及离散和稳定的Stokes方程中生成的线性系统上。我们将TRICG和TRIMR与Symmlq和Minres进行比较，Symmlq和Minres是对称和不确定系统的推荐Krylov方法。在我们的所有实验中，TRICG和TRIMR在基于残留的停止条件下比Symmlq和微小的终止，其迭代次数的提高高达50％。它们还比Block-CG和Block-Minres更可靠地终止。四核和八副精度的实验表明，在TRICG和TRIMR中，基于载体的正交性丧失明显小于块-CG和块中的斜率。
We introduce iterative methods named TriCG and TriMR for solving symmetric quasi-definite systems based on the orthogonal tridiagonalization process proposed by Saunders, Simon and Yip in 1988. TriCG and TriMR are tantamount to preconditioned Block-CG and Block-MINRES with two right-hand sides in which the two approximate solutions are summed at each iteration, but require less storage and work per iteration. We evaluate the performance of TriCG and TriMR on linear systems generated from the SuiteSparse Matrix Collection and from discretized and stablized Stokes equations. We compare TriCG and TriMR with SYMMLQ and MINRES, the recommended Krylov methods for symmetric and indefinite systems. In all our experiments, TriCG and TriMR terminate earlier than SYMMLQ and MINRES on a residual-based stopping condition with an improvement of up to 50% in terms of number of iterations. They also terminate more reliably than Block-CG and Block-MINRES. Experiments in quadruple and octuple precision suggest that loss of orthogonality in the basis vectors is significantly less pronounced in TriCG and TriMR than in Block-CG and Block-MINRES.
