1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
|
// The equation x^3-5*x+1==0 has real roots.
// the graph of this function can be observed here.
xset('window',6);
x=-2:.01:4; // defining the range of x.
deff('[y]=f(x)','y=x^3-5*x+1'); //defining the function.
deff('[y]=fp(x)','y=3*x^2-5');
y=feval(x,f);
a=gca();
a.y_location = "origin";
a.x_location = "origin";
plot(x,y) // instruction to plot the graph
title(' y = x^3-5*x+1')
// from the above plot we can infre that the function has roots between
// the intervals (0,1),(2,3).
// since we have been asked for the smallest positive root of the equation,
// we are intrested on the interval (0,1)
// a=0;b=1,
// since in the example 2.7 we have been asked to perform 4 itterations ,
// the approximate root after 4 iterations can be observed.
newton4(0.5,f,fp)
// hence the approximate root after 4 iterations is 0.201640 witin the permissible error of 10^-15,
|
