A root of a function is known to lie in the bracket

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Numerical and computational mathematics · Numerical and computational mathematics

Computational Physics, Ch Where a function vanishes, and what lies between the points

Problem

A root of a function is known to lie in the bracket [2.0, 5.0] m[2.0,\,5.0]\,\mathrm{m}. Bisection is applied and run for n=25n=25 halvings. (a) State the exact width of the bracket after these 2525 halvings, which bounds the error of any estimate taken from inside it. (b) How many further halvings are needed to guarantee a bracket width below 1.0×10−10 m1.0\times10^{-10}\,\mathrm{m}?

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