roots_and_optimization

Homework #3:

Comparing Different Solvers

solver	initial guess(es)	ea	number of iterations
falsepos	0, 1.5	7.3639e-06	33
bisect	0, 1.5	5.3981e-06	29
newtraph	1	9.8618e-09	5
mod_secant	1	7.9314e-06	10

Plot of convergence for four numerical solvers:

The files used to create the table above are looking for the roots or zeros of the function using the input arguments of an inital guess, the desired relative error, and the maximum number of iterations.

Divergence of Newton-Raphson method

iteration	x_i	approx error
1	2	12.5
2	2	9.5703
3	2	7.8262
4	2	6.6491
5	2	5.7943

Convergene of Newton-Raphson method

iteration	x_i	approx error
1	0.2	1.2e03
2	0.2	1.6531e05
3	0.2	4.5122e11
4	0.2	4.5122e11
5	0.2	4.5122e11

Homework #4

##Script that solves for xc:

for i= 0:90 theta= i*pi/180;

minimum_potential_energy=  @(x_C) 0.5 * x_C*9.81*sin(theta) + 1/2*30 *(0.5 - sqrt(0.5^2+(0.5-x_C)^2))^2;
[C,fx,ea,iter]=goldmin(minimum_potential_energy,0,5,0.00001,50);
x_C(i+1)=C;

end