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A fast solution of banded circulant systems

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Abstract

The solution of banded circulant systems based on structured factorisation is presented. The structured factorisation of banded circulant matrices is obtained by solving a set of non-linear equations. When the matrix is strictly diagonally dominant, the corresponding non-linear system can be solved by an iterative algorithm, e.g., a non-linear SOR or Newton's iteration. Both approaches are presented. The computational complexity of algorithms for computing the structured factorisation depends on the matrix bandwidth and not on its dimensions. A coupled system obtained by the factorisation is solved using a rank-annihilation formula. The structured approach is competitive to the deconvolution one based on the FFT. Moreover, in many practical applications where large matrices with narrow bandwidths occur the structured approach is the most efficient.

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Authors and Affiliations

  1. JoŽef Stefan Institute, Jamova 39, 61111, Ljubljana, Slovenia

    Dušan Caf

  2. Parallel Algorithms Research Centre, Loughborough University of Technology, LE11 3TU, Loughborough, Leics, UK

    David J. Evans

Authors
  1. Dušan Caf
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  2. David J. Evans
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Caf, D., Evans, D.J. A fast solution of banded circulant systems. Journal of VLSI Signal Processing 11, 263–271 (1995). https://doi.org/10.1007/BF02107057

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  • DOI: https://doi.org/10.1007/BF02107057

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