Numerical Stability of Nested Dissection Orderings
نویسندگان
چکیده
Rigorous bounds on rounding errors for sparse positive definite matrices are obtained. When used for nested dissection orderings of finite element matrices, the analysis furnishes bounds which are stronger than those for band orderings.
منابع مشابه
Numerical Stability of Nested Dissection Orderings By Indu
Rigorous bounds on rounding errors for sparse positive definite matrices are obtained. When used for nested dissection orderings of finite element matrices, the analysis furnishes bounds which are stronger than those for band orderings.
متن کاملSPOOLES: An Object-Oriented Sparse Matrix Library
1 Overview Solving sparse linear systems of equations is a common and important component of a multitude of scientific and engineering applications. The SPOOLES software package1 provides this functionality with a collection of software objects and methods. The package provides a choice of three sparse matrix orderings (minimum degree, nested dissection and multisection), supports pivoting for ...
متن کاملComparing Nested Dissection Orderings for Parallel Sparse Matrix Factorization
In this paper we compare nested dissection orderings obtained by diierent graph bisection heuristics. In the context of parallel sparse matrix factorization the quality of an ordering is not only determined by its ll reducing capability, but also depends on the dif-culty with which a balanced mapping of the load onto the processors of the parallel computer can be found. Our analysis shows that ...
متن کاملReducing the ll-in size for an elimination tree
In sparse Cholesky factorization, nding elimination orderings that produce small ll-in is very important and various heuristics have been proposed. For parallel computations, good orderings should produce elimination trees of low height. Finding optimal ll-in orderings and nding optimal height orderings are NP-hard problems. A class of Nested Dissection orderings with minimal separators, has be...
متن کاملTowards an automatic ordering for a symmetric sparse direct solver
In recent years, nested dissection has grown in popularity as the method of choice for computing a pivot sequence for use with a sparse direct symmetric solver. This is particularly true for very large problems. For smaller problems, minimum degree based algorithms often produce orderings that lead to sparser matrix factors. Furthermore, minimum degree orderings are frequently significantly che...
متن کامل