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Bracketing and Bisection
NRiC 9.1 lists some simple bracketing routines.
Once bracketed, root is easy to find by bisection:
- Evaluate f at interval midpoint (a + b) / 2.
- Root must be bracketed by midpoint and whichever a or b gives f of opposite sign.
- Bracketing interval decreases by 2 each iteration:
- Hence to achieve error tolerance of starting from interval of size 0 requires n = log2(0/) steps.