Y12M, Solution of Large and Sparse Systems of Linear Algebraic Euations

Y12M, Solution of Large and Sparse Systems of Linear Algebraic Euations
Zahari Zlatev, Jerzy Wasniewski, Kjeld Schaumburg
Abstract	Solution of Large and Sparse Systems of Linear Algebraic Euations. The Y12M is a package of Fortran Subroutines for the solution of large and sparse systems of linear algebraic equations developed at the Regional Computing Center at the University of Copenhagen (RECKU). Gausian elimination and pivotal strateges are used to factorize the matrix of the systems into two triangular matrices L and U. An attempt to control the magnitude of the non-zero elements in order to avoid overflows or underflows and to detect singularities is carried out during the process of factorization. Iterative refinement of the first solution may be performed. It is verified (by a large set of numerical examples) that iterative refinement combined with a large drop-tolerance and a large stability factor is often very successful when the matrix of the system is sparse. Not only is the accuracy improved but the factorization time is also considerably reduced so that the total computing time for the solution of the system with iterative refinement is less than that without iterative refinement (in some examples tha total computing time was reduced by more than three times). The storage needed can often be reduceced too.
Keywords	Linear Algebraic Euations, Sparse Systems, Iterative refinement
Type	Book [Author]
Year	1981 Vol. 121
Publisher	LNCS, Springer -Verlag
Series	Lecture Notes in Computer Science Nr 121
ISBN / ISSN	ISBN 3-540-10874-2
BibTeX data	[bibtex]
IMM Group(s)	Scientific Computing