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Entranced98 (talk | contribs) Fixed typo |
m task, replaced: Journal für die reine und angewandte Mathematik (Crelle's Journal) → Journal für die reine und angewandte Mathematik |
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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">{{cite book |last1=Henrici |first1=Peter |title=Applied and computational complex analysis. Volume I: Power series- integration-conformal mapping-___location of zeros. |date=1988 |publisher=New York etc.: John Wiley |isbn=0-471-60841-6 |pages=xv + 682 |edition= Repr. of the orig., publ. 1974 by John Wiley \& Sons Ltd., Paperback}}</ref>
<ref>{{cite book |last1=Marden |first1=Morris |title=The geometry of the zeros of a polynomial in a complex variable. |date=1949 |publisher=Mathematical Surveys. No. 3. New York: American Mathematical Society (AMS). |page=148 }}</ref>
It is based on two auxiliary polynomials, introduced by Schur.<ref>{{cite journal |last1=Schur |first1=I |title=Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind. |journal=Journal für die reine und angewandte Mathematik
For a complex polynomial <math>p</math> of [[degree of a polynomial|degree]] <math>n</math> its ''reciprocal adjoint polynomial'' <math>p^{*}</math> is defined by <math>p^{*}(z) = z^{n}\overline{p(\bar{z}^{-1})} </math> and its ''Schurtransform'' <math>Tp</math> by
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