Title: Fast computation of the zeros of a polynomial via factorization of the companion matrix
Authors: Aurentz, Jared L. ×
Vandebril, Raf
Watkins, David S. #
Issue Date: 28-Nov-2013
Publisher: SIAM
Series Title: SIAM Journal on Scientific Computing vol:35 issue:1 pages:A255-A269
Abstract: A new fast algorithm for computing the zeros of a polynomial in $O(n^{2})$ time using $O(n)$ memory is developed. The eigenvalues of the Frobenius companion matrix are computed by applying a nonunitary analogue of Francis's implicitly shifted $QR$ algorithm to a factored form of the matrix. The algorithm achieves high speed and low memory use by preserving the factored form. It also provides a residual and an error estimate for each root. Numerical tests confirm the high speed of the algorithm.
ISSN: 1064-8275
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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