A class of incomplete orthogonal factorization methods. I: methods and theories (1999)
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@MISC{Bai99aclass,
author = {Zhong-Zhi Bai and Iain S. Duff and Andrew J. Wathen},
title = {A class of incomplete orthogonal factorization methods. I: methods and theories},
year = {1999}
}
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Abstract
We study the solution of large sparse nonsingular and unsymmetric systems of linear equations. We present a class of incomplete orthogonal factorization methods based on Givens rotations. These methods include: Incomplete Givens Orthogonalization (IGO-method) and Generalized Incomplete Givens Orthogonalization (GIGO-method), which drop entries from the incomplete orthogonal and upper triangular factors by position; Threshold Incomplete Givens Orthogonalization (TIGO()-method), which drops entries dynamically by their magnitudes; and Generalized Threshold Incomplete Givens Orthogonalization (GTIGO(; p)-method), which drops entries dynamically by both their magnitudes and positions. Theoretical analyses show that these methods can produce a nonsingular sparse incomplete upper triangular factor and either a complete orthogonal factor or a sparse nonsingular incomplete orthogonal factor for a general nonsingular matrix. Therefore, these methods can potentially generate efficient preconditi...
