Talk:Lehmer–Schur algorithm
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[edit]Can anyone find a better reference for the method? I know it only because I made the method up for myself some years ago, only to find last year that it is called Lehmer-Schur - most of what I've seen written on it since is sketchy on the theoretical groundings.
The original reference is D. H. Lehmer, |"A Machine Method for Solving Polynomial Equations", Journal of the ACM, Volume 8, Issue 2 (April 1961),151–162. However, the method proposed in that paper is different from the one described here; Lehmer uses a test by Schur for counting zeros inside circles, instead of using the argument principle on rectangles. Hans Lundmark (talk) 14:14, 23 October 2010 (UTC)
- The content as it is closely resembles Wilf's Global Bisection Algorithm, published 1978 by Herbert S. Wilf as "A Global Bisection Algorithm for Computing the Zeros of Polynomials in the Complex Plane" in Journal of the ACM, vol. 25, no. 3, DOI 10.1145/322077.322084. See also Yakoubsohn 2005 "Numerical analysis of a bisection-exclusion method to find zeros of univariate analytic functions" in Journal of Complexity, vol. 21, no. 5 for a different exclusion method based on the Graeffe iteration.
- And indeed, the characteristics of Lehmers algorithm, the Schur transform of polynomials, the Schur-Cohn test for the number of roots inside the unit disk and the covering of annuli by eight disks of radius 5R/6 each are completely missing in the article.--LutzL (talk) 22:14, 19 December 2013 (UTC)
