Question A1. The table below compares solutions obtained with the Bisection method with those of the Newton Raphson (N-R) routine while finding the root of a function f(x). (a) How many iterations are required for the Bisection method to achieve a solution that is accurate to four significant digits? (b) How many iterations are required for the N-R routine to achieve an accuracy of six significant figures? (c) Using the data provided in the table, estimate the order of convergence for each of the two numerical methods. Iter. | xi Bisection | Eabs Bisection | xi N-R | Eabs N-R 0 | 6.00000E-01 | 2.33E-01 | 6.00000E-01 | 2.33E-01 1 | 8.06139E-01 | 2.65E-02 | 9.04546E-01 | 7.19E-02 2 | 8.30402E-01 | 2.26E-03 | 8.35258E-01 | 2.60E-03 3 | 8.32472E-01 | 1.86E-04 | 8.32662E-01 | 4.04E-06 4 | 8.32643E-01 | 1.53E-05 | 8.32658E-01 | 9.84E-12 5 | 8.32657E-01 | 1.26E-06 | | 6 | 8.32658E-01 | 1.04E-07 | |
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