M.K. Mandal, G. Guo, A.A. Saha, and J.A. Tuszynski (Canada)
Sonar detection, stochastic resonance, global optimization.
This paper compares two deterministic global optimization algorithms widely used for Stochastic resonant(SR) detec tors in sonar applications. The algorithms considered are (i) Brent’s algorithm and (ii) the Piecewise Unimodal al gorithm. Numerical simulations indicate the latter to be two orders of magnitude more efficient than the former, for similar accuracy and oceanic conditions. Computational efficiency is measured by CPU run-time required. This ob servation is explained theoretically by (i) the relative worst case complexities of the two algorithms and (ii) an appro priate normalization property of the Piecewise Unimodal algorithm. Relevant bounds necessary for such theoretical comparisons are derived using standard asymptotic meth ods. A discontinuity in the CPU time required by the Piece wise Unimodal algorithm is explained in terms of a bifur cation of the underlying functional. This discontinuity is thus an inherent (topological) property of the problem and not a manifestation of an underlying numerical instability. These results make it obvious that the Piecewise unimodal algorithm can be used to design real-time and economic upgrades for sonar hardware.
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