Convergence of Bisection Method

Abstract

Fourth roots of the natural numbers from 1 to 30 have been calculated by Bisection method inthe interval [0, 3] using stopping tolerance 0f 0.00001. Calculated roots have been comparedwith the actual values of roots to obtain error and percentage error in the calculated roots.Numerical rate of convergence has also been calculated in the determination of each fourthroot. The highest numerical rate of convergence of Bisection method has been observed in thecalculation of fourth root of 2 and is equal to 1.754385964912. The lowest numerical rate ofconvergence of Bisection method has been observed in the calculation of fourth roots of 1, 3,4-8, 10, 12 and is equal to 1.333333333333. Average error, average percentage error and averagenumerical rate of convergence of Bisection method have been found to be 0.000000062635,0.000003048055 and 1.458082183940 respectively