adding bounds to code, matlab - matlab

Question

I am trying to add bounds to the code but having troubling figuring out where to put them. The equation goes: f(x) = e^(6x) + 1.441e^(2x) − 2.079e^(4x) − 0.333 = 0, -1>=x<=0
function c = newton(x0, delta)
c = x0;
fc = f(x0);
fprintf('initial guess: c=%d, fc=%d\n',c,fc)
if abs(fc) <= delta % check to see if initial guess satisfies
return; % convergence criterion.
end;
while abs(fc) > delta,
fpc = fprime(c);
if fpc==0, % if fprime is 0, abort.
error('fprime is 0') % the error function prints message and exits
end;
c = c - fc/fpc; % Newton step
fc = f(c);
fprintf(' c=%d, fc=%d\n',c,fc)
end;
function fx = f(x)
fx = exp(6*x)+1.441*exp(2*x)-2.079*exp(4*x)-0.333; % Enter your function here.
return;
function fprimex = fprime(x)
fprimex = 6*exp(6*x)+6*exp(2*x)*(ln(2))^2-4*exp(4*x)*ln(8); % Enter the derivative of function
return;

Answer 1

I would add the check after the Newton step. This won't protect against someone entering a -1 or 1 as an initial guess, but that could be done when you do your input validation. I took Ander Biguri's advice and changed the c to x:
function x = newton(x0, delta)
x = x0;
fx = f(x0);
fprintf('initial guess: x=%f, fx=%f\n',x,fx)
if abs(fx) <= delta % check to see if initial guess satisfies
return; % convergence criterion.
end;
while abs(fx) > delta,
fpx = fprime(x);
if fpx==0, % if fprime is 0, abort.
error('fprime is 0') % the error function prints message and exits
end;
x = x - fx/fpx; % Newton step
if( x > 1 || x < -1 )
error('x out of bounds!');
end
fx = f(x);
fprintf(' x=%f, fx=%f\n',x,fx)
end
end
function fx = f(x)
fx = exp(6*x)+1.441*exp(2*x)-2.079*exp(4*x)-0.333; % Enter your function here.
end
function fprimex = fprime(x)
fprimex = 6*exp(6*x)+6*exp(2*x)*(log(2))^2-4*exp(4*x)*log(8); % Enter the derivative of function
end
Here's the output I get:
>> x = newton(0.5, 0.5*1e-4)
initial guess: x=0.500000, fx=8.307733
x=0.375798, fx=2.908518
x=0.263566, fx=1.003444
x=0.165026, fx=0.340291
x=0.081315, fx=0.113210
x=0.012704, fx=0.036909
x=-0.041514, fx=0.011793
x=-0.082894, fx=0.003695
x=-0.113515, fx=0.001136
x=-0.135581, fx=0.000341
x=-0.151084, fx=0.000098
x=-0.161526, fx=0.000025
x =
-0.1615