Abstract:We present a new data structure to approximate accurately and efficiently a polynomial f of degree d given as a list of coefficients f i . Its properties allow us to improve the state-of-the-art bounds on the bit complexity for the problems of root isolation and approximate multipoint evaluation. This data structure also leads to a new geometric criterion to detect ill-conditioned polynomials, implying notably that the standard condition number of the zeros of a polynomial is at least exponential in the number… Show more
“…The remaining case when b = o(d) was solved recently by Moroz [95]. He shows how to isolate the roots of P in time Õ(d(b + log κ)), where κ is a suitable condition number.…”
In this paper, we survey various basic and higher level tasks in computer algebra from the complexity perspective. Particular attention is paid to problems that are fundamental from this point of view and interconnections between other problems.
“…The remaining case when b = o(d) was solved recently by Moroz [95]. He shows how to isolate the roots of P in time Õ(d(b + log κ)), where κ is a suitable condition number.…”
In this paper, we survey various basic and higher level tasks in computer algebra from the complexity perspective. Particular attention is paid to problems that are fundamental from this point of view and interconnections between other problems.
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