The design and use of a sparse direct solver for skew symmetric matrices
نویسنده
چکیده
We consider the direct solution of sparse skew symmetric matrices. We see that the pivoting strategies are similar, but simpler, to those used in the factorization of sparse symmetric indefinite matrices, and we briefly describe the algorithms used in a forthcoming direct code based on multifrontal techniques for the factorization of real skew symmetric matrices. We show how this factorization can be very efficient for preconditioning matrices that have a large skew component.
منابع مشابه
The (R,S)-symmetric and (R,S)-skew symmetric solutions of the pair of matrix equations A1XB1 = C1 and A2XB2 = C2
Let $Rin textbf{C}^{mtimes m}$ and $Sin textbf{C}^{ntimes n}$ be nontrivial involution matrices; i.e., $R=R^{-1}neq pm~I$ and $S=S^{-1}neq pm~I$. An $mtimes n$ complex matrix $A$ is said to be an $(R, S)$-symmetric ($(R, S)$-skew symmetric) matrix if $RAS =A$ ($ RAS =-A$). The $(R, S)$-symmetric and $(R, S)$-skew symmetric matrices have a number of special properties and widely used in eng...
متن کاملNUMERICAL ANALYSIS GROUP PROGRESS REPORT January 1994 – December 1995
2 Sparse Matrices ……………………………………………………………………………… 4 2.1 The direct solution of sparse unsymmetric linear sets of equations (I.S. Duff and J.K. Reid) …………………………………………………………………………… 4 2.2 The design and use of algorithms for permuting large entries to the diagonal 2.6 Element resequencing for use with a multiple front solver (J. A. Scott) ………… 10 2.7 Exploiting zeros on the diagonal in the direct s...
متن کاملA Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
We describe the main features and discuss the tuning of algorithms for the direct solution of sparse linear systems on distributed memory computers developed in the context of PARASOL (ESPRIT IV LTR Project (No 20160)). The algorithms use a multifrontal approach and are especially designed to cover a large class of problems. The problems can be symmetric positive deenite, general symmetric, or ...
متن کاملA NUMA Aware Scheduler for a Parallel Sparse Direct Solver
Over the past few years, parallel sparse direct solvers have made significant progress [1, 3, 4]. They are now able to solve efficiently real-life three-dimensional problems with several millions of equations. Since the last decade, most of the supercomputer architectures are based on clusters of SMP (Symmetric Multi-Processor) nodes. In [5], the authors proposed a hybrid MPI-thread implementat...
متن کامل"Compress and eliminate" solver for symmetric positive definite sparse matrices
We propose a new approximate factorization for solving linear systems with symmetric positive definite sparse matrices. In a nutshell the algorithm is to apply hierarchically block Gaussian elimination and additionally compress the fill-in. The systems that have efficient compression of the fill-in mostly arise from discretization of partial differential equations. We show that the resulting fa...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006