Acceleration of the Inversion of Triangular Toeplitz Matrices and Polynomial Division

Computing the reciprocal of a polynomial in z modulo a power zn 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.

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