上海大学学报（英文版）
上海大學學報（英文版）
상해대학학보（영문판）
JOURNAL OF SHANGHAI UNIVERSITY (ENGLISH EDITION)
2004年
4期
397-405
,共9页
block two-by-two matrix%preconditioner%modified block relaxation iteration%eigenvalue distribution%positive definiteness
For the large sparse block two-by-two real nonsingular matrices, we establish a general framework of structured preconditioners through matrix transformation and matrix approximations. For the specific versions such as modified block Jacobi-type, modified block Gauss-Seidel-type, and modified block unsymmetric (symmetric) Gauss-Seidel-type preconditioners, we precisely describe their concrete expressions and deliberately analyze eigenvalue distributions and positive definiteness of the preconditioned matrices.Also, we show that when these structured preconditioners are employed to precondition the Krylov subspace methods such as GMRES and restarted GMRES, fast and effective iteration solvers can be obtained for the large sparse systems of linear equations with block two-by-two coefficient matrices. In particular, these structured preconditioners can lead to high-quality preconditioning matrices for some typical matrices from the real-world applications.
