Newton Iteration using symbolic function

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emma brooklyn
emma brooklyn on 7 Dec 2021
Answered: Bjorn Gustavsson on 7 Dec 2021
i have write a code for newton iteration method as below;
i got answers in "x" domain. i wanted answer in real numbers
c=2;
syms x
f=x^2-c;
fdx=diff(f)
if fdx==0
disply('Output failure Stop the procedure')
else
x=input('initial condition ='); %initial condition
n=input('Number of iterations = '); %number of iterations
for i=1:n;
x=x-f/fdx;
vpa(x)
end
end

Answers (1)

Bjorn Gustavsson
Bjorn Gustavsson on 7 Dec 2021
Since you use symbolic variables and do the calculations symbolically you will get a symbolic answer.
Here you should convert your function, f, and its derivative to functions. You could do that with the matlab-function matlabFunction. Perhaps something like this:
c=2;
syms x
f=x^2-c;
fdx=diff(f)
if fdx==0
disply('Output failure Stop the procedure')
else
F = matlabFunction(f); % Here we create a dynamical function out of your symbolic expression
dfdx = matlabFunction(fdx); % and its derivative.
x = input('initial condition ='); %initial condition
n = input('Number of iterations = '); %number of iterations
for i1 = 1:n;
x = x - F(x)/dfdx(x); % Call function and its derivative at the point x
X(i1) = x; % Just to save away all points along the iteration
end
end
You should have a thorough look at the help and documentation for function_handle. In this simple case it works out automatically. However, you should preferably not rely on matlabFunction creating functions with some specific ordering of the input parameters, therefore you better check that for real-world use.
HTH

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