FIXED POINT METHOD

For this method it is necessary to convert f(x)=0 into an equitable expression of the form x=g(x), in doing this we will be plotting the line y=x and the curve given by g(x), for the method we first choose the initial x₀, this will be evaluated in g(x) giving a new x₁ since x=g(x), this new x₁ is evaluated in the original function to see if we already find the root f(x)=0, if it is not the case, with the new x₁ we repeat the process evaluating it in g(x) and finding the new x₂, and so on until we find the expected value.

PSEUDOCODE

Input: a, g(x), tolerance.

Error = Tolerance + 1

i=0

While Error > Tolerance

pn= f(a)

Error = ABS( pn – a)

a=pn

i=i+1

print: i,a,pn,error

End

End

CODE

clc;clear

f=input('Enter function with x clear: ','s');

f=inline(f);

a=input('Enter initial value: ');

tol=input('Enter tolerance: ');

e=tol+1;

i=0;

while e>tol

pn=f(a);

e=abs(pn-a);

a=pn;

i=i+1;

fprintf('iter: %2i\t a= %f\t pn= %f\t e= %f\n',i,a,pn,e)

end