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Description: |
We present a method to improve or just guarantee the accuracy of the approximations delivered by any fast method for the eigenvalues of symmetric tridiagonal matrices.
The motivation for this approach is two-folded: 1) the fastest state-of-the-art routines in LAPACK do not always deliver eigenvalues as accurate as they are defined by the data; 2) in some cases it is difficult to estimate the number of correct digits in the computed approximations for the eigenvalues of smaller size. Numerical examples are given to show the effectiveness of the numerical procedure.
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