TY - JOUR
T1 - Further Analysis of Minimum Residual Iterations
AU - Saad, Yousef
PY - 2000
Y1 - 2000
N2 - 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.
AB - 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.
KW - Krylov subspace techniques
KW - Minimal residual methods
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U2 - 10.1002/(SICI)1099-1506(200003)7:2<67::AID-NLA186>3.0.CO;2-8
DO - 10.1002/(SICI)1099-1506(200003)7:2<67::AID-NLA186>3.0.CO;2-8
M3 - Article
AN - SCOPUS:0034403876
SN - 1070-5325
VL - 7
SP - 67
EP - 93
JO - Numerical Linear Algebra with Applications
JF - Numerical Linear Algebra with Applications
IS - 2
ER -