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Acceleration of the Inversion of Triangular Toeplitz Matrices and Polynomial Division

  • Brian J. Murphy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6885)

Abstract

Computing the reciprocal of a polynomial in z modulo a power z n is well known to be closely linked to polynomial division and equivalent to the inversion of an n×n triangular Toeplitz matrix. The degree k of the polynomial is precisely the bandwidth of the matrix, and so the matrix is banded iff k ≪ n. We employ the above equivalence and some elementary but novel and nontrivial techniques to obtain minor yet noticeable acceleration of the solution of the cited fundamental computational problems.

Keywords

Reciprocal of a polynomial modulo a power Polynomial division Triangular Toeplitz matrix inversion Banded triangular Toeplitz matrices 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Brian J. Murphy
    • 1
  1. 1.Department of Mathematics and Computer ScienceLehman College of the City University of New YorkBronxUSA

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