Krylov subspaces and the analytic grade
Typical behaviour of the solution of a linear system of equations obtained iteratively by Krylov methods can be characterized by three stages. Initially the residual diminishes steadily; this is followed by stagnation and finally rapid convergence near the algebraic grade. This study examines this behaviour in terms of the concepts of approximately invariant subspace and what we have called the analytic grade of a Krylov sequence. It is shown how the small Ritz values play a vital role in the convergence and how this knowledge helps in the construction of an effective preconditioner.
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|Item Type:||Journal Article|
|Additional Information:||For more information, please refer to the journal's website (see hypertext link) or contact the author. Author contact details: firstname.lastname@example.org|
|Keywords:||preconditioning, approximately invariant subspaces, convergence, error bounds, Ritz values|
|Subjects:||Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Analysis (010301)|
|Divisions:||Past > QUT Faculties & Divisions > Faculty of Science and Technology|
|Copyright Owner:||Copyright 2005 John Wiley & Sons|
|Deposited On:||22 Jun 2007|
|Last Modified:||29 Feb 2012 13:07|
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