Fast Computation of the Zeros of a Polynomial via Factorization of the Companion Matrix
نویسندگان
چکیده
A new fast algorithm for computing the zeros of a polynomial in O(n2) 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.
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عنوان ژورنال:
- SIAM J. Scientific Computing
دوره 35 شماره
صفحات -
تاریخ انتشار 2013