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For information on the Brent-Dekker algorithm see the following two papers,

- R. P. Brent, “An algorithm with guaranteed convergence for finding a zero of a function”, Computer Journal, 14 (1971) 422–425
- J. C. P. Bus and T. J. Dekker, “Two Efficient Algorithms with Guaranteed Convergence for Finding a Zero of a Function”, ACM Transactions of Mathematical Software, Vol. 1 No. 4 (1975) 330–345