The Mathematical Institute, University of Oxford, Eprints Archive

Incomplete Orthogonal Factorization Methods Using Givens Rotations II: Implementation and Results

Papadopoulos, Andreas T. and Duff, Iain S. and Wathen, A. J. (2002) Incomplete Orthogonal Factorization Methods Using Givens Rotations II: Implementation and Results. Technical Report. Unspecified. (Submitted)

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Abstract

We present, implement and test a series of incomplete orthogonal factorization methods based on Givens rotations for large sparse unsymmetric matrices. These methods include: column-Incomplete Givens Orthogonalization (cIGO-method), which drops entries by position only; column-Threshold Incomplete Givens Orthogonalization (cTIGO-method) which drops entries dynamically by both their magnitudes and positions and where the reduction via Givens rotations is done in a column-wise fashion; and, row-Threshold Incomplete Givens Orthogonalization (r-TIGO-method) which again drops entries dynamically, but only magnitude is now taken into account and reduction is performed in a row-wise fashion. We give comprehensive accounts of how one would code these algorithms using a high level language to ensure efficiency of computation and memory use. The methods are then applied to a variety of square systems and their performance as preconditioners is tested against standard incomplete LU factorization techniques. For rectangular matrices corresponding to least-squares problems, the resulting incomplete factorizations are applied as preconditioners for conjugate gradients for the system of normal equations. A comprehensive discussion about the uses, advantages and shortcomings of these preconditioners is given.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1221
Deposited By:Lotti Ekert
Deposited On:19 May 2011 07:38
Last Modified:19 May 2011 07:38

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