Question

using matlab, and fibonacci. i have included the picture of the function fofx

1. Write a function file to estimate the local maximum or minimum or the function fofx (use the last assignment one for testing) using Golden Section. Inputs are error, and the bounds of the initial interval

i believe problem should say of, not or the function fofx

Matlab is a program to do coding on, Golden Sequence is just Fibonacci

Answer 1

`Hey,

Note: If you have any queries related the answer please do comment. I would be very happy to resolve all your queries.

clc%clears screen
clear all%clears history
close all%closes all files
format long
disp('For minimum');
golden(@fofx,-10,7,1e-5,'min')
disp('For maximum');
golden(@(x) -fofx(x),-10,7,1e-5,'max')
function golden(fofx,a,b,epsilon,s)
iter= 50; % maximum number of iterations
tau=double((sqrt(5)-1)/2); % golden proportion coefficient, around 0.618
k=0; % number of iterations
x1=a+(1-tau)*(b-a); % computing x values
x2=a+tau*(b-a);
f_x1=fofx(x1); % computing values in x points
f_x2=fofx(x2);
while ((abs(b-a)>epsilon) && (k<iter))
k=k+1;
if(f_x1<f_x2)
b=x2;
x2=x1;
x1=a+(1-tau)*(b-a);
  
f_x1=fofx(x1);
f_x2=fofx(x2);
  
else
a=x1;
x1=x2;
x2=a+tau*(b-a);
  
f_x1=fofx(x1);
f_x2=fofx(x2);
  
end
  
k=k+1;
end
% chooses minimum point
if(f_x1<f_x2)
if(strcmp(s,'max'))
f_x1=-f_x1;
end
sprintf('x_%s=%f', s,x1)

sprintf('f(x_%s)=%f ', s,f_x1)
else
if(strcmp(s,'max'))
f_x2=-f_x2;
end
sprintf('x_%s=%f', s,x2)
sprintf('f(x_%s)=%f ', s,f_x2)
end
end
function y=fofx(x)
y=(x.^3+2*x.^2-111*x+108);
end

Kindly revert for any queries

Thanks.