Newton's method problem

clear all; close all;

a=4;
b=3;

x=zeros();

x(1)=1;

for i=1:1000;
 f(x(i))=(x(i)-a)^2+b;  
 x(i+1) =x(i)-(f(x(i))/diff(f(x(i))));
end

[Grzegorz Knor]

Could you describe a problem that you try to solve using this code?

[Andrei Bobrov]

Hi Grzegorz! This is method Newton?

[Prozka]

Yeah

Actually I need to write code for solve optimization problem

using Newtons Method

the problem is

Minimizing the f(x)=(x-4)^2+9

[Walter Roberson]

Code that has a "clear all" statement is broken 99 times out of 100.

Answer 1

[Andrei Bobrov]

for your case EDITED

f = @(x)(x - 4)^2 + 9;
syms x 
ex = (x - 4)^2 + 9;
cf = double(coeffs(ex));
distxp = (4*prod(cf([1 end]))-cf(2)^2)/4/cf(3);
fun = matlabFunction(ex - distxp);
df = matlabFunction(diff(ex));
x = 10;
xout = x;
while abs(fun(x)) > 1e-6
  x1 = x - fun(x)/df(x);
  x = x1;
  xout = [xout;x];
end

ADD corrected

f = @(x)(x - 4)^2 + 9;

syms x 
ex = (x - 4)^2 + 9;
cf = fliplr(double(coeffs(expand(ex))));

distxp = (4*prod(cf([1 end]))-cf(2)^2)/4/cf(1);
fun = @(x)f(x)-distxp;
dcf = polyder(cf);
df = @(x)polyval(dcf,x);
x = 10;
xout = x;
while abs(fun(x)) > 1e-6
    x1 = x - fun(x)/df(x);
    x = x1;
    xout = [xout;x];
end

output for the first 10 iterations and optimal x

if numel(xout)<=10 
   out = xout;
else 
   out = [xout(1:10);xout(end)]; 
end

[Prozka]

How do i get output for the first 10 iterations and optimal x value and solution?

[Prozka]

I am getting error saying that

??? Error using ==> sym.maple at 87

Error, invalid arguments to coeffs

Error in ==> sym.coeffs>coeffsAndTerms at 56

c = maple('coeffs',p,x,'''__ans''');

Error in ==> sym.coeffs at 39

[c,t] = coeffsAndTerms(p,indets);

Error in ==> edited at 4

cf = double(coeffs(ex));

[Andrei Bobrov]

corrected

[Prozka]

thanks

but i need to have iterations run times let say 10000

but output only first 10 iterations of x value and f(x) value

[Andrei Bobrov]

outf = f(out(end))

[Andrei Bobrov]

Proshka, include your head (brain) 10000 iterations is very many

[Prozka]

above case I agree with you we need 10 iterations

but I need to use this code for complex functions

like f(x)=cosx+sin2x+e-x

thanks

Answer 2

[Andreas Goser]

This code isn't working because diff(f(x(i))) returns [] and thus a scalar can't be divide by [].

[Prozka]

Actually I need to write code for solve optimization problem

using Newtons Method

the problem is

Minimizing the f(x)=(x-4)^2+9

Answer 3

[Steve]

You can use this Newton function implementation in general.

function n = newton(f,fp,x0,tol,Nmax)
    n=0;
    test_val = abs(poly_val(f,x0));
    num1 = 1;

      while (test_val > tol && num1<Nmax)
          n = x0 - poly_val(f,x0)/poly_val(fp,x0);
          test_val = abs(poly_val(f,n));
          x0=n;
          num1=num1+1;
      end

end

[Prozka]

how abt poly_val???