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# roots_and_optimization | |
homework 3 | |
i. Compare the number of iterations that each function needed to reach an | |
accuracy of 0.00001%. Include a table in your README.md with: | |
``` | |
| solver | initial guess(es) | ea | number of iterations| | |
| --- | --- | --- | --- | | |
|falsepos | 1,5 | 3.3027 | 1.1363 e-0.7 | | |
|incsearch | 1,5 | 66.2618 | 5.0248 e-0.7 | | |
|newtraph | 1 | 3.4172 e-07 | 802 | | |
|mod_secant | 1 | 0.0014 | 3 | | |
``` | |
![Plot of convergence for four numerical solvers.](https://github.uconn.edu/chv14004/roots_and_optimization/blob/master/convergence.png) | |
convergence of the four different methods falsepos, bisect, newtraph and mod_secant being used to solve for the angle of the projecitle function with an initial velocity of 15 m/s. the approximated error is being plotted against the number of iterations | |
### divergence of Newton-Raphson method | |
| iteration | x_i | approx error | | |
| - | -- | --- | | |
| 0 | 2 | n/a | | |
| 1 | 2 | 12.5000 | | |
| 2 | 2 | 9.5703 | | |
| 3 | 2 | 7.8262 | | |
| 4 | 2 | 6.6491 | | |
| 5 | 2 | 5.7943 | | |
| - | -- | --- | | |
| 0 | 0.2 | n/a | | |
| 1 | 0.2 | 1.2500 e+0.3 | | |
| 2 | 0.2 | 1.6531 e+0.5 | | |
| 3 | 0.2 | 4.5122 e+11 | | |
| 4 | 0.2 | 4.5122 e+11 | | |
| 5 | 0.2 | 4.5122 e+11 | | |
Homework #4 | |
![Steady-state position of collar on rod at angle theta](https://github.uconn.edu/chv14004/roots_and_optimization/blob/master/untitled.png) | |