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Further analysis of minimum residual iterations
Author(s) -
Saad Yousef
Publication year - 2000
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/(sici)1099-1506(200003)7:2<67::aid-nla186>3.0.co;2-8
Subject(s) - residual , mathematics , chebyshev polynomials , convergence (economics) , linear subspace , chebyshev filter , chebyshev nodes , mathematical optimization , algorithm , pure mathematics , mathematical analysis , economics , economic growth
The convergence behaviour of a number of algorithms based on minimizing residual norms over Krylov subspaces is not well understood. Residual or error bounds currently available are either too loose or depend on unknown constants that can be very large. In this paper we take another look at traditional as well as alternative ways of obtaining upper bounds on residual norms. In particular, we derive inequalities that utilize Chebyshev polynomials and compare them with standard inequalities. Copyright © 2000 John Wiley & Sons, Ltd.