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:
    • n+1 = n / 2.
  • Hence to achieve error tolerance of  starting from interval of size 0 requires n = log2(0/) steps.

Notes: