Reorthogonalization for Golub–kahan–lanczos Bidiagonal Reduction: Part Ii – Singular Vectors
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چکیده
where U ∈ R is left orthogonal, V ∈ R is orthogonal, and B ∈ R is bidiagonal. When the Lanczos recurrence is implemented in finite precision arithmetic, the columns of U and V tend to lose orthogonality, making a reorthogonalization strategy necessary to preserve convergence of the singular values. A new strategy is proposed for recovering the left singular vectors. When using that strategy, it is shown that, in floating point arithmetic with machine unit εM , if orth(V ) = ‖I − V T V ‖2,
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Reorthogonalization for the Golub-Kahan-Lanczos bidiagonal reduction
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تاریخ انتشار 2010