How can I change the definition of x to find the value of y(3.5112)( i mean y(x1)) for this question ?

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Answers (1)

Torsten
Torsten on 1 Aug 2022
I don't know if it helps:
%%main func
clear all;
close all;
clf;
clc;
% Define the function
x = linspace(-10,10,100);
f = @Goldenfunc;
y = f(x);
figure(1)
plot(x,y,'k',LineWidth=2), hold on
xr = GoldenSection(0,10,f);
plot(xr,'bo')
function [xr] = GoldenSection(xL,xU,y)
N = 200;
GR = (sqrt(5)-1) / 2; % Golden Ratio Number
d = GR * (xU-xL);
x1 = xL + d;
x2 = xU - d;
fx1 = y(x1); % y(x1) alamıyor çünkü x1 positive integer değil
fx2 = y(x2);
for i=1:N
if fx1 > fx2 % Move lower bound to x1
xL = x1;
fL = fx1;
x1 = x2; % update x1
fx1 = fx2;
d = GR * (xU - xL); %update d & x2
x2 = xL + d;
fx2 = y(x2);
elseif fx1 < fx2
xU = x2;
fU = fx2;
x2 = x1;
fx2 = fx1;
d = GR * (xU - xL); %update d & x1
x1 = xU - d;
fx1 = y(x1);
else
xL = (x1 + x2) / 2;
xU = xL;
end
end
xr = (x1 + x2) / 2;
%plot(xr,'ko')
end
function y = Goldenfunc(x)
%x = linspace(0,10,100);
y = x.^2 - 6*x + 15;
%plot(x,y);
%hold on
end
  1 Comment
Torsten
Torsten on 1 Aug 2022
Edited: Torsten on 1 Aug 2022
This would me my suggestion:
%%main func
% Define the function
x = linspace(-10,10,100);
y = f(x);
figure(1)
plot(x,y,'k',LineWidth=2)
hold on
a = 0;
b = 10;
fun = @f;
tol = 1e-8;
x = GoldenSection(a,b,fun,tol);
plot(x,f(x),'o')
function x = GoldenSection(a,b,f,tol)
GR = (sqrt(5)+1) / 2; % Golden Ratio Number
c = b - (b - a) / GR;
d = a + (b - a) / GR;
while abs(b - a) > tol
if f(c) < f(d) % f(c) > f(d) to find the maximum
b = d;
else
a = c;
end
% We recompute both c and d here to avoid loss of precision which may lead to incorrect results or infinite loop
c = b - (b - a) / GR;
d = a + (b - a) / GR;
end
x = (a+b)/2;
end
function y = f(x)
y = x.^2 - 6*x + 15;
end

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