blob: a9c11018718c2a481b469ad783b3a0c486cfec93 (
plain)
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
31
32
33
34
35
36
|
// The equation cos(x)-x*%e^x==0 has real roots.
// the graph of this function can be observed here.
xset('window',25);
x=0:.01:2; // defining the range of x.
deff('[y]=f(x)','y=cos(x)-x*%e^x'); //defining the cunction.
y=feval(x,f);
a=gca();
a.y_location = "origin";
a.x_location = "origin";
plot(x,y) // instruction to plot the graph
title(' y = cos(x)-x*%e^x')
// from the above plot we can infre that the function has root between
// the interval (0,1)
x0=0;
//solution using linear iteration method for the first two iterations and aitken's process two times for the third iteration.
deff('[y]=g(x)','y=x+1/2*(cos(x)-x*%e^x)');
deff('[y]=gp(x)','y=1+1/2*(-sin(x)-x*%e^x-%e^x)');
generaliteration2(x0,g,gp)
// from the above iterations performed we can infer that-
x1=0.50000000;
x2=0.5266110;
aitken(x0,x1,x2,g) // calling the aitken method for one iteration
|
