codings for layer Program 13.1 Golden Section Search for minimum of f(x)

Start with unimodal f(x) and minimum in [a,b]

Input: inline function f, interval [a,b], number of steps k

Output: approximate minimum y

function y=gss(f,a,b,k)

g=(sqrt(5)-1)/2

x1 = a+(1-g)*(b-a)

x2 = a+g*(b-a)

f1=f(x1) f2=f(x2)

for i=1:k

if f1 < f2 if f(x1) < f(x2), replace b with x2

b=x2 x2=x1 x1=a+(1-g)*(b-a)

f2=f1 f1=f(x1) single function uation

else otherwise, replace a with x1

a=x1 x1=x2 x2=a+g*(b-a)

f1=f2 f2=f(x2) single function uation

end

end

y=(a+b)/2 -codings for layer　Program 13.1 Golden Section Search for minimum of f(x)

　Start with unimodal f(x) and minimum in [a,b]

　Input: inline function f, interval [a,b], number of steps k

　Output: approximate minimum y

function y=gss(f,a,b,k)

g=(sqrt(5)-1)/2

x1 = a+(1-g)*(b-a)

x2 = a+g*(b-a)

f1=f(x1) f2=f(x2)

for i=1:k

　if f1 < f2　　　　　　if f(x1) < f(x2), replace b with x2

　　b=x2　x2=x1　x1=a+(1-g)*(b-a)

　　f2=f1　f1=f(x1)　　 single function　uation

　else　　　　　　　　　otherwise, replace a with x1

　　a=x1　x1=x2　x2=a+g*(b-a)

　　f1=f2　f2=f(x2)　　 single function　uation

　end

end

y=(a+b)/2