Theory and Modern Applications
Table 15 \(f_{10}(x)= \frac{ (1+\sqrt {1-4 x})^{2}}{4}+2 x \ln ( \vert \frac{1-\sqrt {1-4 x}}{2} \vert )\)
From: Generalization of the bisection method and its applications in nonlinear equations
Methods | IT | \(x_{n}\) | \(f(x_{n})\) | δ |
|---|---|---|---|---|
\(\mathrm{QBM}_{a}\) | 57 | 0.2036321887945368 | 1.110223e − 16 | −2.22044e − 16 |
\(\mathrm{QBM}_{b}\) | 51 | 0.2036321887945368 | 1.110223e − 16 | 0 |
\(\mathrm{QBM}_{c}\) | 59 | 0.2036321887945370 | −4.440892e − 16 | −1.4988e − 15 |
Bisection | 49 | 0.2036321887945370 | −2.220446e − 16 | 3.053113e − 16 |
Regula falsi | 22 | 0.2036321887945373 | −8.881784e − 16 | −1.22124e − 15 |
Newton–Raphson | 6 | 0.203632188794537 | 1.11022e − 16 | 1.72703e − 10 |