# Newton-Raphson

### Keerthi venkateswara Rao (view profile)

29 Dec 2003 (Updated )

Newton-Raphson method for all real roots of the polynomial.

newton(coeff_function,initial_guess,error_tolerance,max_iterations)
```% this m-file calculates the real roots of the given polynomial using
% newton raphson technique.this m-file calls the functions in the two m-files named as syn_division and
% derivate.
% coeff_function is the 1xn matrix conatining the coeff of the polynomial.
% Keerthi Venkateswara Rao
function [final_roots,functionvalue] = newton(coeff_function,initial_guess,error_tolerance,max_iterations)
iterations=0;
max_no_roots=size(coeff_function,2);
final_roots=0;
functionvalue=0;
for no_roots=1:max_no_roots-1
fun_root_new=initial_guess;
flag=1;
coeff_der_function=derivate(coeff_function);
order_fun=size(coeff_function,2);
order_der_fun=size(coeff_der_function,2);
while flag==1
fun_root_old=fun_root_new;
fx=0;
dfx=0;
nonzero=1;
while nonzero==1
powers=order_fun-1;
for index=1:order_fun
fx=fx+coeff_function(index)*fun_root_old^powers;
powers=powers-1;
end
powers=order_der_fun-1;
for index=1:order_der_fun
dfx=dfx+coeff_der_function(index)*fun_root_old^powers;
powers=powers-1;
end
if dfx==0
fun_root_old=fun_root_old+1;
else
nonzero=0;
end
end
iterations = iterations + 1;
fun_root_new = fun_root_old - fx/dfx;
if iterations >= max_iterations
flag=0;
elseif  abs(fun_root_new-fun_root_old)<=error_tolerance
flag=0;
final_roots(no_roots)=fun_root_new;
functionvalue(no_roots)=fx;
end
end
coeff_function=syn_division(coeff_function,fun_root_new);
end
```