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Calcolo

, Volume 52, Issue 1, pp 25–43 | Cite as

The palindromic cyclic reduction and related algorithms

  • Bruno Iannazzo
  • Beatrice Meini
Article

Abstract

The cyclic reduction algorithm is specialized to palindromic matrix polynomials and a complete analysis of applicability and convergence is provided. The resulting iteration is then related to other algorithms as the evaluation/interpolation at the roots of unity of a certain Laurent matrix polynomial, the trapezoidal rule for a certain integral and an algorithm based on the finite sections of a tridiagonal block Toeplitz matrix.

Keywords

Cyclic reduction Trapezoidal rule Gauss–Chebyshev quadrature Matrix geometric mean Matrix sign Matrix square root Polar decomposition Laurent matrix polynomial 

Mathematics Subject Classification

65F30 15A15 

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Copyright information

© Springer-Verlag Italia 2014

Authors and Affiliations

  1. 1.Dipartimento di Matematica e InformaticaUniversità di PerugiaPerugiaItaly
  2. 2.Dipartimento di MatematicaUniversità di PisaPisaItaly

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