Abstract.
In this paper, we consider shifted tridiagonal matrices. We prove that the standard algorithm to compute the LU factorization in this situation is mixed forward-backward stable and, therefore, componentwise forward stable. Moreover, we give a formula to compute the corresponding condition number in O(n) flops.
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This research has been partially supported by Dirección General de Investigación (Ministerio de Ciencia y Tecnología) of Spain through grants BFM2003-06335-C03-02 and MTM2006-06671 as well as by the Postdoctoral Fellowship EX2004-0658 provided by Ministerio de Educación y Ciencia of Spain.
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Brittin, C., Bueno, M.I. Numerical Properties of Shifted Tridiagonal LU Factorizations. MedJM 4, 277–290 (2007). https://doi.org/10.1007/s00009-007-0118-x
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DOI: https://doi.org/10.1007/s00009-007-0118-x