| Citation: | GU Tong-xiang, CHI Xue-bin, LIU Xing-ping. AINV and BILUM Preconditioning Techniques[J]. Applied Mathematics and Mechanics, 2004, 25(9): 927-934. | 
	                | [1] | 
					 Saad Y.Iterative Methods for Sparse Linear Systems[M].New York:PWS Publishing, 1996. 
					
					 | 
			
| [2] | 
					 Golub G H,van der Vorst H A.Closer to the solution: iterative linear solver[A].In:Duff I S,Watson G A Eds.The State of the Art in Numerical Analysis[C]:Oxford: Clarendon Press,1997,63—92. 
					
					 | 
			
| [3] | 
					 Saad Y,ZHANG Jun.BILUM: block versions of multi-elimination and multi-level ILU preconditioner for general sparse linear systems[J].SIAM J Sci Comput,1999,20(6):2103—2121. doi:  10.1137/S106482759732753X 
					
					 | 
			
| [4] | 
					 Benzi M,Tuma M.A sparse approximate inverse preconditioner for nonsymmetric linear systems[J].SIAM J Sci Comput,1998,19(3):968—994. doi:  10.1137/S1064827595294691 
					
					 | 
			
| [5] | 
					 Chan T F.TANG Wei-pai,Wan W L.Wavelet sparse approximate inverse preconditioners[J].BIT, 1997,37(3):644—660. doi:  10.1007/BF02510244 
					
					 | 
			
| [6] | 
					 Chow E,Saad Y.Approximate inverse techniques for block-partitioned matrices[J].SIAM J Sci Comput,1997,18(6):1657—1675. doi:  10.1137/S1064827595281575 
					
					 | 
			
| [7] | 
					 Chow E,Saad Y.Approximate inverse preconditioner via sparse-sparse iterations[J].SIAM J Sci Comput,1998,19(3):995—1023. doi:  10.1137/S1064827594270415 
					
					 | 
			
| [8] | 
					 Gould N I M.Scott J A.Sparse approximate-inverse preconditioners using norm minimization techniques[J].SIAM J Sci Comput,1998,19(2):605—625. doi:  10.1137/S1064827595288425 
					
					 | 
			
| [9] | 
					 Grote M,Huckle T.Parallel preconditioning with sparse approximate inverses[J].SIAM J Sci Comput,1997,18(3):838—853. doi:  10.1137/S1064827594276552 
					
					 | 
			
| [10] | 
					 Saad Y.ILUT: a dual threshold incomplete ILU preconditioner[J].Numer Linear Algebra Appl,1994,1(4):387—402. doi:  10.1002/nla.1680010405 
					
					 | 
			
| [11] | 
					 TANG Wei-pai,Wan W L.Sparse approximate inverse smoother for multigrid[J].SIAM J Matrix Anal Appl,2000,21(4):1236—1252. doi:  10.1137/S0895479899339342 
					
					 | 
			
| [12] | 
					 Saad Y,ZHANG Jun.Enhanced multi-level block ILU preconditioning strategies for general linear systems[J].J Comput Appl Math,2001,130(1/2):99—118. doi:  10.1016/S0377-0427(99)00388-X 
					
					 | 
			
| [13] | 
					 ZHANG Jun.Sparse approximate inverse and multilevel block ILU preconditioning techniques for general sparse matrices[J].Appl Numer Math,2000,35(1):67—86. doi:  10.1016/S0168-9274(99)00047-1 
					
					 | 
			
| [14] | 
					 Benzi M,Tuma M.A comparative study of sparse approximate inverse preconditioners[J].Appl Numer Math,1999,30(2/3):305—340. doi:  10.1016/S0168-9274(98)00118-4 
					
					 | 
			
| [15] | 
					 Benzi M,Meyer C D,Tuma M.A sparse approximate inverse preconditioner for the conjugate gradient method[J].SIAM J Sci Comput,1996,17(5):1135—1149. doi:  10.1137/S1064827594271421 
					
					 | 
			
| [16] | 
					 Benzi M,Cullum J K,Tuma M.Robust approximate inverse preconditioning for the conjugate gradient method[J].SIAM J Sci Comput,2000,22(4):1318—1332. doi:  10.1137/S1064827599356900 
					
					 | 
			
| [17] | 
					 Benzi M,Tuma M.Orderings for factorized sparse approximate inverse preconditioners[J].SIAM J Sci Comput,2000,21(5):1851—1868. doi:  10.1137/S1064827598339372 
					
					 | 
			
| [18] | 
					 Kolotina L Y,Yeremin A Y.Factorized sparse approximate inverse preconditioningⅠ: theory[J].SIAM J Matrix Anal Appl,1993,14(1):45—58. doi:  10.1137/0614004 
					
					 | 
			
| [19] | 
					 Saad Y.ILUM:a multi-elimination ILU preconditioner for general sparse matrices[J].SIAM J Sci Comput,1996,17(4):830—847. doi:  10.1137/0917054 
					
					 | 
			
| [20] | 
					 Saad Y,Sosonkina M,ZHANG Jun.Domain decomposition and multi-level type techniques for general sparse linear systems[A].In:Mandel J,Farhat C,Cai X C,Eds.Domain Decomposition Methods 10[C].number 218 in Contemporary Mathematics, Providence, RI, AMS,1998,174—190. 
					
					 | 
			
| [21] | 
					 Saad Y.A flexible inner-outer preconditioned GMRES algorithm[J].SIAM J Sci Comput,1993,14(2):461—469. doi:  10.1137/0914028 
					
					 | 
			
| [22] | 
					 Saad Y,ZHANG Jun.BILUTM:a domain-based multi-level block ILUT preconditioner for general linear systems[J].SIAM J Matrix Anal Appl,1999,21(1):279—299. doi:  10.1137/S0895479898341268 
					
					 | 
			
| [23] | 
					 ZHANG Jun.On convergence of iterative methods with a fourth-order compact scheme[J].Appl Math Lett,1997,10(2):49—55. 
					
					 |