HP MLIB User's Guide Vol. 2 7th Ed.

876 HP MLIB User’s Guide
Chapter objectives
Chapter objectives
After you read this chapter you will:
• Understand what sparse systems are
• Understand how to use these subprograms to solve linear systems and to
estimate condition numbers
• Understand issues in choosing an optimal method for a specific problem
This sparse matrix linear equation software makes it possible to call a single
subprogram to solve a single system of sparse linear equations. However, this
requires a particular format for the sparse matrix.
This package provides other approaches that provide a general interface to
alternative representations of the sparse matrix, and also make available
underlying capabilities for reducing the cost of solving multiple sparse systems.
These optional approaches require the user to call a sequence of subprograms.
Associated documentation
The following documents provide supplemental material for this chapter:
Ashcraft, C.C. “A Vector Implementation of the Multifrontal Method for Large
Sparse, Symmetric Positive Definite Linear Systems.” Boeing Computer
Services Technical Report ETA-TR-51. 1987.
Ashcraft, C.C. and R.G. Grimes. “The Influence of Relaxed Supernode
Partitions on the Multifrontal Method.” ACM Transactions on Mathematical
Software. December, 1989. Vol. 15, No. 4. pp 291-309.
Ashcraft, C.C., R.G. Grimes, J.G. Lewis, B.W. Peyton, and H.D. Simon.
“Progress in Sparse Matrix Methods for Large Linear Systems on Vector
Supercomputers.” The International Journal of Supercomputer Applications.
1987. Vol. 1, No. 4. pp. 10-30.
Duff, I.S., A.M. Erisman, and J.K. Reid. Direct Methods for Sparse Methods.
Oxford, England: Clarendon Press. 1986.
Duff, I.S. and J.K. Reid. “The Multifrontal Solution of Indefinite Sparse
Symmetric Linear Equations.” ACM Transactions of Mathematical Software.
September, 1983. Vol. 9, No. 3. pp. 302-325.