TY - JOUR

T1 - Simple algorithms for approximating all roots of a polynomial with real roots

AU - Ben-Or, Michael

AU - Tiwari, Prasoon

PY - 1990/12

Y1 - 1990/12

N2 - We present a simple algorithm for approximating all roots of a polynomial p(x) when it has only real roots. The algorithm is based on some interesting properties of the polynomials appearing in the Extended Euclidean Scheme for p(x) and p′(x). For example, it turns out that these polynomials are orthogonal; as a consequence, we are able to limit the precision required by our algorithm in intermediate steps. A parallel implementation of this algorithm yields a P-uniform NC2 circuit, and the bit complexity of its sequential implementation is within a polylog factor of the bit complexity of the best known algorithm for the problem.

AB - We present a simple algorithm for approximating all roots of a polynomial p(x) when it has only real roots. The algorithm is based on some interesting properties of the polynomials appearing in the Extended Euclidean Scheme for p(x) and p′(x). For example, it turns out that these polynomials are orthogonal; as a consequence, we are able to limit the precision required by our algorithm in intermediate steps. A parallel implementation of this algorithm yields a P-uniform NC2 circuit, and the bit complexity of its sequential implementation is within a polylog factor of the bit complexity of the best known algorithm for the problem.

UR - http://www.scopus.com/inward/record.url?scp=0000294842&partnerID=8YFLogxK

U2 - 10.1016/0885-064X(90)90032-9

DO - 10.1016/0885-064X(90)90032-9

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AN - SCOPUS:0000294842

SN - 0885-064X

VL - 6

SP - 417

EP - 442

JO - Journal of Complexity

JF - Journal of Complexity

IS - 4

ER -