Question

given values are correct. only need missing values.

(1 point) Starting with a--1, b = 1, do 4 iterations of golden section search to estimate wheref(x)-(x2-sin(4 * x)) reaches a minimum. f(c) f(d) 0.236068 0.23607 0.236068 0.23607 0.52786 0.75434 0.57873 2 -0.236068 0.527864 3 0.527864 0.23607 0.34752 -0.75434 -0.86295 0.34752 -0.86295

Answer 1

SOLUTION

i-value	a	b	c	d	f(c)	f(d)
0	-1	1	-0.2361	0.23607	0.8658	-0.75434
1	-0.2361	1	0.23607	0.52786	-0.75434	-0.57873
2	-0.2361	0.52786	0.05573	0.23607	-0.21797	-0.75434
3	0.05573	0.52786	0.23607	0.34752	-0.75434	-0.86295
4	0.23607	0.52786	0.34752	0.41641	-0.86295	-0.82211

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Matlab Code: Create a new file f.m with the following code

function y=f(x)

y=x^2-sin(4*x);

Now do the following in the matlab terminal.

figure; hold on;

a=-1; % start of interval

b=1; % end of interval

epsilon=0.000001; % accuracy value

iter= 5; % 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=f(x1); % computing values in x points

f_x2=f(x2);

plot(x1,f_x1,'rx') % plotting x

plot(x2,f_x2,'rx')

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=f(x1)

f_x2=f(x2)

  

plot(x1,f_x1,'rx')

else

a=x1

x1=x2

x2=a+tau*(b-a)

  

f_x1=f(x1)

f_x2=f(x2)

plot(x2,f_x2,'rx')

end

end