Theory and Modern Applications
Table 3 Calculations of \(h_{i}\) and \(f(h_{i})\) for \(i=1,2,3\) and different values of q using QBM
From: Generalization of the bisection method and its applications in nonlinear equations
q | \(h_{1}\) | \(f(h_{1})\) | \(h_{2}\) | \(f(h_{2})\) | \(h_{3}\) | \(f(h_{3})\) |
|---|---|---|---|---|---|---|
0.1 | 8.181818182 | −50.951149 | 8.347107438 | −41.670069 | 8.497370398 | −32.472823 |
0.2 | 8.333333333 | −42.476596 | 8.611111111 | −25.016891 | 8.842592593 | −8.488212 |
0.25 | 8.400000000 | −38.516300 | 8.720000000 | −17.471052 | 8.976000000 | 1.886054 |
0.3 | 8.461538462 | −34.732872 | 8.816568047 | −10.438809 | 9.089667729 | 11.228232 |
0.4 | 8.571428571 | −27.667180 | 8.979591837 | 2.174127 | 8.688046647 | −19.727211 |
0.5 | 8.666666667 | −21.217337 | 9.111111111 | 13.043294 | 8.814814815 | −10.569367 |
0.528 | 8.691099476 | −19.513166 | 9.143389710 | 15.807306 | 8.847388248 | −8.126180 |
0.55 | 8.709677419 | −18.203730 | 9.167533819 | 17.899858 | 8.872142593 | −6.244585 |
0.6 | 8.750000000 | −15.320925 | 9.218750000 | 22.410246 | 8.925781250 | −2.093276 |
0.65 | 8.787878788 | −12.561745 | 9.265381084 | 26.601946 | 8.975985753 | 1.884912 |
0.7 | 8.823529412 | −9.919360 | 9.307958478 | 30.500635 | 9.023000204 | 5.692251 |
0.8 | 8.888888889 | −4.959450 | 9.382716049 | 37.512245 | 9.108367627 | 12.810134 |
0.85 | 8.918918919 | −2.630066 | 9.415631848 | 40.667177 | 9.147138373 | 16.130788 |
0.9 | 8.947368421 | −0.393742 | 9.445983380 | 43.613282 | 9.183554454 | 19.300255 |
0.909 | 8.952331063 | −0.000690 | 9.451194900 | 44.122723 | 9.189872827 | 19.855175 |
1 | 9 | 3.819700 | 8.5 | −32.305300 | 8.75 | −15.320925 |