An improved method for one-way dissection with singular diagonal blocks
- Pennsylvania State Univ., University Park, PA (USA). Dept. of Computer Science
We consider matrices arising out of the one-way dissection method for solving large sparse systems of linear equations. The systems that we consider are those that may have singular diagonal blocks. Such systems arise in certain fluid flow problems. Gunzberger and Nicholaides proposed a method for resolving the singularity in the diagonal blocks. This method uses the Moore-Penrose pseudoinverse. We propose two improvements to the Gunzberger-Nicholaides procedure: the substitution of a weighted pseudoinverse for the Moore-Penrose pseudoinverse; a more elegant implementation of the back substitution procedure. A stability analysis of both our procedure and the Gunzberger-Nicholaides procedure is given. Both our analysis and empirical tests show that our method has better numerical stability properties than the Gunzberger-Nicholaides procedure. We also implement our procedure on Intel iPSC/1 Hypercube. Our improvement to the back substitution method makes the natural parallelism in the problem easier to exploit. 13 refs., 2 tabs.
- Research Organization:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Sponsoring Organization:
- USDOD; DOE/ER; National Science Foundation (NSF)
- DOE Contract Number:
- AC05-84OR21400
- OSTI ID:
- 7091115
- Report Number(s):
- ORNL/TM-11477; ON: DE90012041; CNN: CCR-8700172; AFOSR-88-0161; N0014-80-0517; N00024085-C-6041
- Country of Publication:
- United States
- Language:
- English
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