solve eq by newton raphson method

i want to write a script that will calculate for solution of equation :

3x+sin(x)-exp(x)=0

with Newton Raphsons method algorithm.

[Walter Roberson]

http://www.mathworks.com/matlabcentral/answers/6200-tutorial-how-to-ask-a-question-on-answers-and-get-a-fast-answer

Answer 1

[Radu Trimbitas]

Solve the equation with Newton-Raphson method.

Define function and derivative

format long
f=@(x) 3*x+sin(x)-exp(x);
df=@(x) 3+cos(x)-exp(x);

Explore the roots graphically

fplot(f,[-pi,pi])
grid on

Find a solution within [0,1]

x0=0;
[z1,ni]=Newton(f,df,x0,1e-8,1e-8,20)

Find a solution within [1,2]

x0=1.5;
[z2,ni]=Newton(f,df,x0,1e-8,1e-8,20)

Check the roots

f([z1,z2])

Code for Newton-Raphson method. It also works for nonlinear systems.

function [z,ni]=Newton(f,fd,x0,ea,er,nmax)
%NEWTON - Newton ethod for nonlinear equations and systems
%call [z,ni]=Newton(f,fd,x0,ea,er,nmax)
%Input
%f - function
%fd - derivative or Jacobian
%x0 - starting value or vector 
%ea - absolute error
%er - relative error
%nmax - maximum # iterations
%Iesire
%z - approximate root
%ni - actual # iterations

if nargin < 6, nmax=50; end
if nargin < 5, er=0; end
if nargin < 4, ea=1e-3; end
xp=x0(:);   %x precedent
for k=1:nmax
    xc=xp-fd(xp)\f(xp); 
    if norm(xc-xp,inf)<ea+er*norm(xc,inf)
        z=xc; %success
        ni=k;
        return
    end
    xp=xc;
end
error('Iterations # exceeded');
end