Durand–Kerner method: Difference between revisions

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{{Short description|Root-finding algorithm for polynomials}}

{{refstyle|date=November 2020}}

In [[numerical analysis]], the '''Weierstrass method''' or '''Durand–Kerner method''', discovered by [[Karl Weierstrass]] in 1891 and rediscovered independently by Durand in 1960 and Kerner in 1966, is a [[root-finding algorithm]] for solving [[polynomial]] [[equation (mathematics)|equations]].<ref name="Petković">{{cite book |last1=Petković |first1=Miodrag |title=Iterative methods for simultaneous inclusion of polynomial zeros |date=1989 |publisher=Springer |___location=Berlin [u.a.] |isbn=978-3-540-51485-5 |pages=31–32}}</ref> In other words, the method can be used to solve numerically the equation ''f''(''x''){{=}}0, where ''f'' is a given polynomial, which can be taken to be scaled so that the leading coefficient is&nbsp;1.

: ''f''(''x'') = 0,

where ''f'' is a given polynomial, which can be taken to be scaled so that the leading coefficient is&nbsp;1.

==Explanation==