A stability analysis of incomplete $LU$ factorizations
نویسندگان
چکیده
منابع مشابه
A Stability Analysis of Incomplete LU Factorizations
The combination of iterative methods with preconditionings based on incomplete LU factorizations constitutes an effective class of methods for solving the sparse linear systems arising from the discretization of elliptic partial differential equations. In this paper, we show that there are some settings in which the incomplete LU preconditioners are not effective, and we demonstrate that their ...
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When solving large linear systems of equations arising from the discretization of elliptic boundary value problems, a combination of iterative methods and preconditioners based on incomplete LU factorizations is frequently used. Given a model problem with variable coefficients, we investigate a class of incomplete LU factorizations depending on a relaxation parameter. We show that the associate...
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This paper addresses the problem of computing preconditioners for solving linear systems of equations with a sequence of slowly varying matrices. This problem arises in many important applications. For example, a common situation in computational fluid dynamics, is when the equations change only slightly, possibly in some parts of the physical domain. In such situations it is wasteful to recomp...
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This paper addresses the problem of computing preconditioners for solving linear systems of equations with a sequence of slowly varying matrices. This problem arises in many important applications. For example, a common situation in computational fluid dynamics, is when the equations change only slightly, possibly in some parts of the physical domain. In such situations it is wastful to recompu...
متن کاملIncremental Incomplete LU factorizations with applications to time-dependent PDEs
A common problem which arises in many complex applications is to solve a sequence of linear systems of the form: Akxk = bk, for k = 1, 2, .. In these applications Ak does not generally change too much from one step k to the next, as it is often the result of a continuous process (e.g. Ak can represent the discretization of some problem at time tk.) We are faced with the problem of solving each ...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1986
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1986-0842130-7