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A fast modified sine transform for solving block-tridiagonal systems with Toeplitz blocks

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Abstract

In this report we consider block-tridiagonal systems with Toeplitz blocks. Each block is of sizen×n consisting ofn c×n c matrices as entries, and there arem×m blocks in the system. The solution of those systems consists of 2n c m modified sine transforms and an intermediate solution ofn block-tridiagonal systems. Symmetries in the data vectors are exploited such that one modified sine transform can be computed in terms of one Fourier transform of half the length of the original one, hence requiringO(2.5nlog2 n) operations. Similarly, we only have to solve (n+1)/2 of the intermediate systems due to symmetry.

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Authors and Affiliations

  1. Department of Scientific Computing, Uppsala University, Box 120, S-751 04, Uppsala, Sweden

    Lina Hemmingsson

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  1. Lina Hemmingsson
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Communicated by Å. Björck

This work was supported by the Swedish National Board for Industrial and Technical Development, NUTEK, under contract No. 89-02539 P.

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Hemmingsson, L. A fast modified sine transform for solving block-tridiagonal systems with Toeplitz blocks. Numer Algor 7, 375–389 (1994). https://doi.org/10.1007/BF02140691

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  • DOI: https://doi.org/10.1007/BF02140691

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