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- W3087888411 abstract "We design shifted LR transformations based on the integrable discrete hungry Toda equation to compute eigenvalues of totally nonnegative matrices of the banded Hessenberg form. The shifted LR transformation can be regarded as an extension of the extension employed in the well-known dqds algorithm for the symmetric tridiagonal eigenvalue problem. In this paper, we propose a new and effective shift strategy for the sequence of shifted LR transformations by considering the concept of the Newton shift. We show that the shifted LR transformations with the resulting shift strategy converge with order 2 − e for arbitrary e > 0." @default.
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- W3087888411 date "2020-09-07" @default.
- W3087888411 modified "2023-10-14" @default.
- W3087888411 title "Convergence acceleration of shifted $LR$ transformations for totally nonnegative Hessenberg matrices" @default.
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- W3087888411 doi "https://doi.org/10.21136/am.2020.0378-19" @default.
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