Lehmer–Schur algorithm: Difference between revisions

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In [[mathematics]], the '''Lehmer-SchurLehmer–Schur algorithm''' (named after [[Derrick Henry Lehmer]] and [[Issai Schur]]) is a [[root-finding algorithm]] extending the one-dimensional bracketing used by the [[bisection method]] to find the roots of a function of one complex variable inside any rectangular region of the function's [[Holomorphic function|holomorphicity]] (''i.e.'', [[Analytic function|analyticity]]).

The rectangle in question is quadrisected into four, [[Congruence (geometry)|congruent]] quarter rectangles. The [[argument principle]] is then applied to the boundary of each quarter to find the [[winding number]] (about the origin) for the boundary. Given that the function is [[Analytic function|analytic]] within each of these quarters, a nonzero [[winding number]] ''N'' (always an integer) identifies ''N'' zeros of the function inside the quarter in question, each zero counted as many times as its [[multiplicity]].