Problem of unstable pivots in the incomplete LU-conjugate gradient method
Incomplete LU and incomplete-Cholesky conjugate gradient methods are becoming widely used in both laser and magnetic fusion research. In my original presentation of these methods, the problem of what to do if a pivot (L/sub ii/U/sub ii/) becomes very small or zero was raised and only partially answered by the suggestion that it be arbitrarily set to some non-zero value. In what follows it will be shown precisely how small the pivot can become before it must be fixed and precisely what value it should be set to in order to minimize the error in LU. Numerical examples will be given to show that not only does this prescription improve incomplete LU-conjugate gradient methods , but exact LU decomposition carried out with this prescription for handling small pivots and followed by a few linear or conjugate gradient iterations can be much faster than the permutations of rows and columns usually employed to circumvent small pivot problems.
- Research Organization:
- California Univ., Livermore (USA). Lawrence Livermore Lab.
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 6917482
- Report Number(s):
- UCRL-81103; CONF-780614-1
- Country of Publication:
- United States
- Language:
- English
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