Summary.
This paper presents a new efficient algorithm for solving bidiagonal systems of linear equations on massively parallel machines. We use a divide and conquer approach to compute a representative subset of the solution components after which we solve the complete system in parallel with no communication overhead. We address the numerical properties of the algorithm in two ways: we show how to verify the à posteriori backward stability at virtually no additional cost, and prove that the algorithm is à priori forward stable. We then show how we can use the algorithm in order to bound the possible perturbations in the solution components.
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Received March 13, 1998 / Revised version received December 21, 1999 / Published online June 20, 2001
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Bar-On, I., Leoncini, M. Reliable parallel solution of bidiagonal systems. Numer. Math. 90, 415–440 (2002). https://doi.org/10.1007/s002110100296
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DOI: https://doi.org/10.1007/s002110100296