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02_roots_and_optimization

Repository for homework 2

Question 2

cat_cable = @(T) -35+T/10.*cosh(10./T*30)+30-T/10;
[root,fx,ea,iter]=falsepos(cat_cable,900,910,0.00001)
cat_cable = @(T) -35+T/10.*cosh(10./T*30)+30-T/10;
[root,fx,ea,iter]=bisect(cat_cable,908,909,0.00001)
cat_cable = @(T) -35+T/10.*cosh(10./T*30)+30-T/10;
[root,ea,iter]=mod_secant(cat_cable,900,910,0.00001)
| solver | initial guess | ea | number of iterations|
| --- | --- | --- | --- |
|falsepos   | 900, 910 |  0.00001| 4  |
|mod_secant | 900, 910 |  0.00001| 50 |
|bisect     | 900, 910 |  0.00001| 17 |

Powerline Plot

Question 3

f = @(x) (x-1)*exp(-(x-1)^2);
df = @(x) -(2*(x)^2-4*x+1)*exp(-(x-1)^2);
[root,ea,iter]=newtraph(f,df,3,.00001,5)
### divergence of Newton-Raphson method

| iteration | x_i | approx error |
| --- | --- | --- |
| 0 | 3 |    n/a    |
| 1 | 3 |   8.6957  |
| 2 | 3 |   6.8573  |
| 3 | 3 |   5.7348  |
| 4 | 3 |   4.9605  |
| 5 | 3 |   4.3873  |
### convergence of Newton-Raphson method

| iteration | x_i | approx error |
| --- | --- | --- |
| 0 |  1.2 |     n/a       |
| 1 |  1.2 |   22.1239     |
| 2 |  1.2 |    1.7402     |
| 3 |  1.2 |    0.0011     |
| 4 |  1.2 |    2.3315e-13 |
| 5 |  1.2 |    2.3315e-13 |