the question is: Create a function which finds the root of an equation numerically by using the following recursive formula :

Xn+1=Xn-f(Xn)/g(Xn) for n-1,2,3,...
where g(Xn)=f(Xn+f(Xn))-f(Xn)/f(Xn). This iterative procedure must stop when the absolute difference between Xn and Xn+1 is less than a given tolerance epsilon. The funtion must accept as inputs a scalar function f, an initial number 'x' and a positive number epsilon to terminate the procedure. Hence use this numerical technique to find the root of the equation e^x-x^2=0.

HELP PLEASE :(

syms x
f=exp(x)-x^2;
y(1)=1;
if x(n)-x(n+1)<0.25;
for n=0:1:inf;
x(k+1)=yk-subs(f,x,yk)/subs(g(xn),x,yk);
where g(xn)=(f(xn+f(xn))-f(xn))/(f(xn))
end
end

[Walter Roberson]

(A) That is an iterative procedure that is described, not a recursive procedure;

(B) MATLAB does not have any "where" command;

(C) Your x is symbolic, so x(n) is symbolic, making it unlikely that the difference between the two will be numeric so that the difference can be tested in the "if" statement.

[Brittany Roland]

so how shall i arrange this to make it work ?

[Walter Roberson]

syms x g(xn) f(x)
f(x) = exp(x)-x^2;
g(xn) = (f(xn+f(xn))-f(xn))/(f(xn));

That takes care of the "where" part.

Note: this requires a fairly recent version of MATLAB, R2011b or later.

[Brittany Roland]

it is still not working however because of the 6th line :(

Answer 1

[Friedrich]

Hi,

why using symblic math when doing it nurmerically anyway? You can do this with plain MATLAB right away:

f = @(x) exp(x) - x^2;
g = @(x) (f(x + f(x)) - f(x))/f(x);

x(1) = 0;
x(2) = x(1) - f(x(1))/g(x(1));
n = 2;
while abs(x(n) - x(n-1)) > eps
    n = n + 1;
    x(n) = x(n-1) - f(x(n-1))/g(x(n-1));
end

[Friedrich]

You can check the result with:

>> sprintf('%0.16f \n',f(x(end-1)))

ans =

-0.0000000000000002 

>> sprintf('%0.16f \n',f(x(end)))

ans =

0.0000000000000000

[Brittany Roland]

Thanks so much !.. if you really want like a challenge, you should try figure out another of my questions by clicking the link: http://www.mathworks.com/matlabcentral/answers/75189-please-help-in-this-question-how-to-change-this-sentence-into-mathematical-terms

:)