how can I use fzero to this equation?

P(x)=polyfit(x,y,7)

Answer 1

[Star Strider]

This is how I would do it:

x = -9:9;                                               % Create Data
y = x.^3 - 2;                                           % Create Data

p = polyfit(x,y,7);                                     % Fit Polynomial

f = @(x,p) cos(sqrt(abs(polyval(p,x)))) - sin(x)/2;     % Function

f_root = fzero(@(x) f(x,p), 1)                          % Find Root

[mar vouz]

if I had to create a mFile I would write :

function y=f(x,p)
y=cos(sqrt(abs(polyval(p,x)))) - sin(x)/2;
end

and then in the main file I would have to write

f_root=fzero(@(x) f(x,p),1)

is this correct?

[mar vouz]

Also I forgot to mention that I have to find the possitive root which is closest to 0. So in f_root=fzero(@(x) f(x,p),1) after comma I should put 1 or 0?

[Star Strider]

First, yes, that is correct. I would use the anonymous function unless you absolutely have to create a function .m-file. If you ware going to save it as a function file, I would rename the function to something other than ‘f’, perhaps something more descriptive such as ‘polyfun’ or something, so the function becomes:

function y=polyfun(x,p)
y=cos(sqrt(abs(polyval(p,x)))) - sin(x)/2;
end

that you would save as polyfun.m, then call it as:

f_root=fzero(@(x) polyfun(x,p),1)

Second, starting it at 0 is appropriate.

[mar vouz]

unfortunatly when I use 0,f_root is negative !

[Star Strider]

You may have to iterate initial parameter estimates in a for loop to find the closest root to zero.

Example:

xv0 = linspace(0, 5, 100);                              % Vector Of Initial Estimates
for k1 = 1:length(xv0)
    f_root(k1) = fzero(@(x) f(x,p), xv0(k1));           % Find Root
end

roundn = @(x,n) round(x .* 10.^n)./10.^n;               % Round ‘x’ To ‘n’ Digits, Emulates Latest ‘round’ Function

function_roots = unique(roundn(f_root, 4));             % Find Unique Roots

I used my roundn function (use round if it allows rounding to a specific number of decimal places, as it does in the most recent MATLAB releases) to guarantee unique roots. Choose the one closest to zero.

Note that fzero finds only real roots. The Optimization Toolbox function fsolve will find complex roots, but you have to give it a complex initial estimate to get it to look for them (at least in my experience with it).

[mar vouz]

thank you very much everyone!

[Star Strider]

My pleasure!

The most sincere expression of thanks here on MATLAB Answers is to Accept the Answer that most closely solves your problem.