# Newtonbad.m -- Example of cycle

Cf. Moler: NCM Ch. 4.3 A perverse example

```Condition for cycle: x(n+1) - a = -(x(n) -a)
Holds if f'(x)/f(x) = 1/(2(x-a)), integrating:
f(x) = sign(x-a)sqrt(abs(x-a))```
```close all
newt1=@(f,df,x) x-f(x)/df(x)
a=2;
f=@(x) sign(x-a).*sqrt(abs(x-a))
ezplot(f,[0 4])
grid on; hold on
df=@(x) 1/2/sqrt(abs(x-a))
disp('Choose starting point')
[x0,y0]=ginput(1)
xcurr=x0;
X=[];
N=5;
for k=1:N
X=[X xcurr];
xcurr=newt1(f,df,xcurr)
disp('ENTER continues')
text(1,1.5,'ENTER continues')
pause()
plot([X(end) X(end) xcurr],[0 f(X(end)) 0],'-.r')
%       old xcurr   new xcurr
shg
if k <=3
text(X(end),-0.1,num2str(k-1))
end
end
```
```newt1 =

function_handle with value:

@(f,df,x)x-f(x)/df(x)

f =

function_handle with value:

@(x)sign(x-a).*sqrt(abs(x-a))

df =

function_handle with value:

@(x)1/2/sqrt(abs(x-a))

Choose starting point

x0 =

0.8710

y0 =

-1.1336

xcurr =

3.1290

ENTER continues

xcurr =

0.8710

ENTER continues

xcurr =

3.1290

ENTER continues

xcurr =

0.8710

ENTER continues

xcurr =

3.1290

ENTER continues
```