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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Acceleration of the Inversion of Triangular Toeplitz Matrices and Polynomial Division
verfasst von : Brian J. Murphy
Erschienen in: Computer Algebra in Scientific Computing
Verlag: Springer Berlin Heidelberg
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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.