Paper Info
Title
On Iom(Q): The Incomplete Orthogonalization Method For Large Unsymmetric Linear Systems
Abstract
The incomplete orthogonalization method (IOM(q)), a truncated version of the full orthogonalization method (FOM) proposed by Saad, has been used for solving large unsymmetric linear systems. However, no convergence analysis has been given. In this paper, IOM(q) is analysed in detail from a theoretical point of view. A number of important results are derived showing how the departure of the matrix A from symmetry affects the basis vectors generated by IOM(q), and some relationships between the residuals for IOM(q) and FOM are established. The results show that IOM(q) behaves much like FOM once the basis vectors generated by it are well conditioned. However, it is proved that IOM(q) may generate an ill-conditioned basis for a general unsymmetric matrix such that IOM(q) may fail to converge or at least cannot behave like FOM. Owing to the mathematical equivalence between IOM(q) and the truncated ORTHORES(q) developed by Young and Jea, insights are given into the convergence of the latter. A possible strategy is proposed for choosing the parameter q involved in IOM(q). Numerical experiments are reported to show convergence behaviour of IOM(q) and of its restarted version.
Year
DOI
Venue
1996
10.1002/(SICI)1099-1506(199611/12)3:6<491::AID-NLA87>3.0.CO;2-9
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
Keywords
Field
DocType
unsymmetric, Krylov subspace, IOM(q), FOM, truncated, basis vector, orthonormality, convergence, restarted
Convergence (routing),Krylov subspace,Mathematical optimization,Orthonormality,Linear system,Matrix (mathematics),Equivalence (measure theory),Orthogonalization,Basis (linear algebra),Mathematics
Journal
Volume
Issue
ISSN
3
6
1070-5325
Citations 
PageRank 
References 
1
0.37
6
Authors
1
Name
Order
Citations
PageRank
Zhongxiao Jia112118.57