The Mathematical Institute, University of Oxford, Eprints Archive

A class of incomplete orthogonal factorization methods. I: methods and theories

Bai, Zhong-Zhi and Duff, Iain S. and Wathen, A. J. (1999) A class of incomplete orthogonal factorization methods. I: methods and theories. Technical Report. B I T. (Submitted)

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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($\tau$)-method), which drops entries dynamically by their magnitudes; and Generalized Threshold Incomplete Givens Orthogonalization (GTIGO($\tau,p$)-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 preconditioners for Krylov subspace methods for solving large sparse systems of linear equations. Moreover, the upper triangular factor is an incomplete Cholesky factorization preconditioner for the normal equations matrix from least-squares problems.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1288
Deposited By:Lotti Ekert
Deposited On:01 Jun 2011 09:19
Last Modified:01 Jun 2011 09:19

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