Four novel multi-phase hybrid bracketing algorithms for numerical root finding: Opt.BF (mpbf), Opt.BFMS (mpbfms), Opt.TF (mptf), Opt.TFMS (mptfms). Combines classical methods with modified secant for superior convergence (e.g., mptfms averages 2.3 iterations). Reference DOI: 10.21608/joems.2026.440115.1078
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