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function b = fzerosimp(xl,xu)
a = xl; b = xu; fa = f(a); fb = f(b);
c = a; fc = fa; d = b - c; e = d;
while (1)
if fb == 0, break, end
if sign(fa) == sign(fb) %If needed, rearrange points
a = c; fa = fc; d = b - c; e = d;
end
if abs(fa) < abs(fb)
c = b; b = a; a = c;
fc = fb; fb = fa; fa = fc;
end
m = 0.5*(a - b); %Termination test and possible exit
tol = 2 * eps * max(abs(b), 1);
if abs(m) <= tol | fb == 0.
break
end
%Choose open methods or bisection
if abs(e) >= tol & abs(fc) > abs(fb)
s = fb/fc;
if a == c %Secant method
p = 2*m*s;
q = 1 - s;
else %Inverse quadratic interpolation
q = fc/fa; r = fb/fa;
p = s * (2*m*q * (q - r) - (b - c)*(r - 1));
q = (q - 1)*(r - 1)*(s - 1);
end
if p > 0, q = -q; else p = -p; end;
if 2*p < 3*m*q - abs(tol*q) & p < abs(0.5*e*q)
e = d; d = p/q;
else
d = m; e = m;
end
else %Bisection
d = m; e = m;
end
c = b; fc = fb;
if abs(d) > tol, b=b+d; else b=b-sign(b-a)*tol; end
fb = f(b);
end
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