2012 **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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“…The application of the bisection method on the logarithmic scale seems to be an often forgotten technique within the different communities that make use of numerical solvers, and it is certainly under-represented in the literature. We surveyed popular numerical analysis and optimization textbooks, including Boyd and Vandenberghe [3], Chapra and Canale [6], Gill et al [7], Luenberger and Ye [8], Press et al [10], and found no reference to this technique, despite the existence of scattered references in computational forums 2 and other isolated references to "geometric bisection" in the context of eigenvalue computation [11,12]. In fact, it is easy to find textbook examples that recommend the use of relative error stopping criteria in conjunction with bisection method on a linear scale (see pseudo-code in Figure 5.11 of [6] and chapter 9.1 of [10]).…”

confidence: 99%

“…The application of the bisection method on the logarithmic scale seems to be an often forgotten technique within the different communities that make use of numerical solvers, and it is certainly under-represented in the literature. We surveyed popular numerical analysis and optimization textbooks, including Boyd and Vandenberghe [3], Chapra and Canale [6], Gill et al [7], Luenberger and Ye [8], Press et al [10], and found no reference to this technique, despite the existence of scattered references in computational forums 2 and other isolated references to "geometric bisection" in the context of eigenvalue computation [11,12]. In fact, it is easy to find textbook examples that recommend the use of relative error stopping criteria in conjunction with bisection method on a linear scale (see pseudo-code in Figure 5.11 of [6] and chapter 9.1 of [10]).…”

confidence: 99%