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

Michael Ben-Or*, Prasoon Tiwari

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

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.

Original languageAmerican English
Pages (from-to)417-442
Number of pages26
JournalJournal of Complexity
Volume6
Issue number4
DOIs
StatePublished - Dec 1990

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