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Aberth method
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<p>The Aberth method, or Aberth–Ehrlich method or Ehrlich–Aberth method, named after Oliver Aberth and Louis W. Ehrlich, is a <a href="/facts/Root-finding_algorithm/IxTDkhBq">root-finding algorithm</a> developed in 1967 for simultaneous approximation of all the roots of a <a href="/facts/Univariate_polynomial/Lzak8VVx">univariate polynomial</a>. </p><p>This method converges cubically, an improvement over the <a href="/facts/Durand%25E2%2580%2593Kerner_method/TleuAKMv">Durand–Kerner method</a>, another algorithm for approximating all roots at once, which converges quadratically. (However, both algorithms converge linearly at <a href="/facts/Multiplicity_(mathematics)/dndUyetA">multiple zeros</a>.) </p><p>This method is used in <a href="/facts/MPSolve/aB3W3Lqb">MPSolve</a>, which is the reference software for approximating all roots of a polynomial to an arbitrary precision. </p>