Approximate and Incomplete Factorizations
Approximate and Incomplete Factorizations
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DOI：
10.1007/978-94-011-5412-3_6
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发表时间：
1997
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影响因子：
--
通讯作者：
T. Chan;H. V. D. Vorst
中科院分区：
文献类型：
--
作者：
T. Chan;H. V. D. Vorst
In this chapter, we give a brief overview of a particular class of preconditioners known as incomplete factorizations. They can be thought of as approximating the exact LU factorization of a given matrix A (eg, computed via Gaussian elimination) by disallowing certain fill-ins. As opposed to other PDE-based preconditioners such as multigrid and domain decomposition, this class of preconditioners is primarily algebraic in nature and can in principle be applied to general sparse matrices. vVhen applied to PDE problems, they are usually not optimal in the sense that the condition number of the preconditioned system grows as the mesh size h is reduced, although usually at a slower rate than for the unpreconditioned system. On the other hand, they are often quite robust with respect to other more algebraic features of the problem such as rough and anisotropic coefficients and strong convection terms. We will describe the basic ILU and (modified) rvIILU preconditioners. Then we will review briefly several variants: more fill, relaxed Ill.!. shifted ILU, ILQ, as well as block and multilevel variants.\Ve will also touch on a related class of approximate factoriza-lThe work of this aut. hor was part. ially supported by t. he National Science Foundat. ion uncler contract. ASC 92-01266, the Army Research Office under contract. s DAAL03-91-G-0150 and DAALOJ-91-C-0047 (Univ. Tenn. subcontract. ORA4466. 04 Amendment I), and the Office of Naval Research under cont. ract. ON R-N00014-92-J-1890.
