volume 219, issue 4, P1607-1615 2012
DOI: 10.1016/j.amc.2012.08.002
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Rui Ralha

Abstract: Bisection (of a real interval) is a well known algorithm to compute eigenvalues of symmetric matrices. Given an initial interval [a, b], convergence to an eigenvalue which has size much smaller than a or b may be made considerably faster if one replaces the usual arithmetic mean (of the end points of the current interval) with the geometric mean. Exploring this idea, we have implemented geometric bisection in a Matlab code. We illustrate the effectiveness of our algorithm in the context of the computation of t…

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