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{{Short description|Root-finding algorithm}}
In [[mathematics]], the '''Lehmer–Schur algorithm''' (named after [[Derrick Henry Lehmer]] and [[Issai Schur]]) is a [[root-finding algorithm]] for [[complex polynomial]]s, extending the idea of enclosing roots like in the one-dimensional [[bisection method]] to the complex plane. It uses the Schur-Cohn test to test increasingly smaller disks for the presence or absence of roots.
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<ref name="Henrici" />
.<ref>{{cite journal |last1=Stewart |first1=G.W.III |title=On Lehmer's method for finding the zeros of a polynomial. |journal=Math. Comput. |date=1969 |volume=23 |issue=108 |pages=829–835 |doi=10.2307/2004970|jstor=2004970 }}</ref>
To avoid extreme scaling, or just for the sake of efficiency, one may start with testing a number of concentric disks for the number of included roots and thus reduce the region where roots occur to a number of narrow
<ref>{{cite journal |last1=Loewenthal |first1=Dan |title=Improvement on the Lehmer-Schur root detection method. |journal=J. Comput. Phys. |date=1993 |volume=109 |issue=2 |pages=164–168 |doi=10.1006/jcph.1993.1209|bibcode=1993JCoPh.109..164L }}</ref>
Finally, when a small disk is found that contains a single root, that root may be further approximated using other methods, e.g. [[Newton's method]].
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{{Reflist}}
▲[[Category:Root-finding algorithms]]
[[Category:Polynomial factorization algorithms]]
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