In this paper, we study a parallel-in-time (PinT) algorithm for all-at-oncesystem from a non-local evolutionary equation with weakly singular kernel . We propose to use a two-sided preconditioning technique for theall at-once discretization of the equation . This is the first attempt to develop a PinTpreconditioning technique that has fast and exact implementation and that the .responding Preconditioned system has a uniformly bounded . condition number is proven to be uniformly bounded by a constant independent of the matrix size . Exploiting thediagonalizability of the constant-Laplacian matrix and . the triangular Toeplitzstructure of the temporal discretification matrix, we obtain efficientrepresentations of inverses of the right and the left preconditionsers, we obtained efficient representations of the inversations of . the right . to the right or the left pre-conditioning matrix, they obtain efficientRepresentations of Inverses and the matrix . Theoretically, the condition

Author(s) : Xue-lei Lin, Michael K. Ng, Yajing Zhi

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Keywords : matrix - equation - system - bounded - obtain -

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