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roots_and_optimization/HW3_Script.m
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%HW_3 | |
%Script calls functions and outputs tables and plots relevant to HW3. | |
[root1,fx1,ea1,iter1]=falsepos(@(x) projectile(x),1,50,.00001); | |
[root2,ea2,iter2]=mod_secant(@(x) projectile(x),1,50,.00001); | |
[root3, ea3, iter3]= newtraph(@(x) projectile(x),@(x) dprojectile_dtheta(x),50,.00001,1000); | |
[root4,fx4,ea4,iter4]=bisect(@(x) projectile(x),0,50,.00001); | |
%Question 1: part (i) | |
%for loop creates data table for given outputs above | |
for n=1:4; | |
Table(n,1)=root(n); | |
Table(n,2)=ea(n); | |
Table(n,3)=iter(n); | |
Table(n,4)=fx(n); | |
end | |
%Question 1: part(ii) | |
%Plots the graphs that compare methods | |
e_b = 1; | |
e_f = 2; | |
e_n = 3; | |
e_m = 4; | |
for n = 1:iter1 | |
[r, y, e_b(n), k] = falsepos(@(x) projectile(x),1,50,.00001); | |
end | |
for n = 1:iter2 | |
[r, y, e_f(n)] = mod_secant(@(x) projectile(x),1,50,.00001); | |
end | |
for n = 1:iter3 | |
[r, e_n(n), k] = newtraph(@(x) projectile(x),@(x) dprojectile_dtheta(x),50,.00001,1000); | |
end | |
for n = 1:iter4 | |
[r, e_m(n), k] = bisect(@(x) projectile(x),0,50,.00001); | |
end | |
%Plot | |
%This section sets up the code inorder to plot the data. | |
setdefaults | |
plot(1:iter1, e_b, 'g', 1:iter2, e_f, 'b', 1:iter3, e_n, 'r', 1:iter4, e_m, 'y') | |
title('Approx Err. of Convergent Functions vs Number of Iterations'); | |
xlabel('Iteration'); | |
ylabel('Approx Error'); | |
legend('bisect','falsepos', 'newtraph', 'mod secant'); |