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.

Reliable Parallel Solution of Bidiagonal Systems / I., BAR ON; Leoncini, Mauro. - In: NUMERISCHE MATHEMATIK. - ISSN 0029-599X. - STAMPA. - 90(2002), pp. 415-440.

Reliable Parallel Solution of Bidiagonal Systems

LEONCINI, Mauro
2002

Abstract

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.
90
415
440
Reliable Parallel Solution of Bidiagonal Systems / I., BAR ON; Leoncini, Mauro. - In: NUMERISCHE MATHEMATIK. - ISSN 0029-599X. - STAMPA. - 90(2002), pp. 415-440.
I., BAR ON; Leoncini, Mauro
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/454035
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