Key Concepts For Parallel Out-Of-Core LU Factorization

Jack J. Dongarra - Sven Hammarling - David W. Walker

March 28, 1996

Abstract:

This paper considers key ideas in the design of out-of-core dense LU factorization routines. A left-looking variant of the LU factorization algorithm is shown to require less I/O to disk than the right-looking variant, and is used to develop a parallel, out-of-core implementation. This implementation makes use of a small library of parallel I/O routines, together with ScaLAPACK and PBLAS routines. Results for runs on an Intel Paragon are presented and interpreted using a simple performance model.

• Introduction
• Sequential Out-Of-Core LU Factorization
  • Right-Looking Algorithm
  • Left-Looking Algorithm
• Implementation of the Left-Looking Algorithm
• Approaches To Parallel I/O
• Parallel I/O Routines For Dense Matrices
  • File Management Routines
  • I/O Routines
  • Auxiliary Routines
  • Implementation Issues
• A Parallel Algorithm
• Performance Results
• Summary and Conclusions
• References
• About this document ...