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2000

Analysis of the finite precision bi-conjugate gradient algorithm for nonsymmetric linear systems

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Analysis of the finite precision bi-conjugate gradient algorithm for nonsymmetric linear systems
In this paper we analyze the bi-conjugate gradient algorithm in finite precision arithmetic, and suggest reasons for its often observed robustness. By using a tridiagonal structure, which is preserved by the finite precision bi-conjugate gradient iteration, we are able to bound its residual norm by a minimum polynomial of a perturbed matrix (i.e. the residual norm of the exact GMRES applied to a perturbed matrix) multiplied by an amplification factor. This shows that occurrence of near-breakdowns or loss of biorthogonality does not necessarily deter convergence of the residuals provided that the amplification factor remains bounded. Numerical examples are given to gain insights into these bounds.
Charles H. Tong, Qiang Ye
Added 19 Dec 2010
Updated 19 Dec 2010
Type Journal
Year 2000
Where MOC
Authors Charles H. Tong, Qiang Ye
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