A comparative study of null-space factorizations for sparse symmetric saddle point systems
نویسندگان
چکیده
منابع مشابه
The null-space method and its relationship with matrix factorizations for sparse saddle point systems
The null-space method for solving saddle point systems of equations has long been used to transform an indefinite system into a symmetric positive definite one of smaller dimension. A number of independent works in the literature have identified the equivalence of the null-space method and matrix factorizations. In this report, we review these findings, highlight links between them, and bring t...
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We will present theory that underpins the use of null-space preconditioners, giving eigenvalue bounds that show that the eigenvalues of the preconditioned system are clustered when a good approximation to the null-space matrix can be found. Additionally, we will describe how two of the family of preconditioners, although indefinite and non-symmetric, can be applied with a Krylov method with a s...
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Saddle-point systems appear in many scientific and engineering applications. The systems can be sparse, symmetric or nonsymmetric, and possibly singular. In many of these applications, the number of constraints is relatively small compared to the number of unknowns. The traditional null-space method is inefficient for these systems, because it is expensive to find the null space explicitly. Som...
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ژورنال
عنوان ژورنال: Numerical Linear Algebra with Applications
سال: 2017
ISSN: 1070-5325
DOI: 10.1002/nla.2103