Newton Method using Matlab Code

Hey guys so i attempted to program the newton iteration

f is the function, f_prime the derivative, x_0 is the start value, epsilon is the stop criteria

I tried this with newton(sin(i),cos(i),x_0,10.^(-6)) but got the error message:

Index exceeds matrix dimensions.
Error in newton (line 4)
while abs(f(nullstelle(i))<epsilon); 

Matlab Code:

function [x] = newton(f,f_prime,x_0,epsilon)
x(1) = x_0;
i = 1;
while abs(f(x(i))<epsilon);
    x(i+1) = x(i) - f(x(i))/f_prime(x(i))
    i = i + 1;
end

2 Questions - firstly does the code make sense. Secondly if i want to run the function, does my command make sense?

Answer 1

[Matt J]

You need to pass function handles to the objective and its derivative,

newton(@sin,@cos,x_0,10.^(-6))

and the while loop continuation criterion should look like

while abs(f(x(i)) > epsilon
    
    
end

[Rohit Sil]

Thank you Matt!

[Rohit Sil]

@Matt, one more question

if i want to enter a function like the one below.

f(x) = x.^5 − 14x.^4 + x.^2 − 3x + 5

how would that be done? also through function handles?

I tried it as it is and got a message saying that x is undefined...

[Jan]

@Rohit: Exactly, you need function handles again:

f = @(x) x.^5 - 14 * x.^4 + x.^2 - 3 * x + 5;

and equivalently for the derivative.

Answer 2

[Oguz ODABAS]

f = inline (x^4 + 2*x^3-23*x^2+12*x+36);

fd = inline (4*x^3 + 6*x^2 - 46*x + 12);

x = -10:0.01:10;

y = f(x);

x0 = -10;

while abs (f(x0))> 1.0e-6;

x1 = x0 - (f(x0)/fd(x0));

x0 = x1;

end

[Oguz ODABAS]

error: for x^y, only square matrix arguments are permitted and one argument must be scalar. Use .^ for elementwise p

ower.

error: called from

Octave13 at line 1 column 3