Chebyshev Semi−iteration in Preconditioning

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It is widely believed that Krylov subspace iterative methods are better than Chebyshev semi-iterative 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 semi-iterative method, which requires eigenvalue bounds and computes an explicit polynomial,...

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Authors: Wathen, T

• Publisher: Oxford University Computing Laboratory
• Publication date: 2008-10-01