Rees, Tyrone and Wathen, A. J. (2008) Chebyshev semiiteration in Preconditioning. Technical Report. Unspecified. (Submitted)

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Abstract
It is widely believed that Krylov subspace iterative methods are better than Chebyshev semiiterative methods. When the solution of a linear system with a symmetric and positive definite coefficient matrix is required then the Conjugate Gradient method will compute the optimal approximate solution from the appropriate Krylov subspace, that is, it will implicitly compute the optimal polynomial. Hence a semiiterative method, which requires eigenvalue bounds and computes an explicit polynomial, must, for just a little less computational work, give an inferior result. In this manuscript we identify a specific situation in the context of preconditioning when the Chebyshev semiiterative method is the method of choice since it has properties which make it superior to the Conjugate Gradient method.
Item Type:  Technical Report (Technical Report) 

Subjects:  H  N > Numerical analysis 
Research Groups:  Numerical Analysis Group 
ID Code:  1064 
Deposited By:  Lotti Ekert 
Deposited On:  21 Apr 2011 07:32 
Last Modified:  29 May 2015 18:45 
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