嵌套乘法的计算：
\[P(x) = 1 - x + x^2 - x^3 + ...+ x ^ {98} - x^{99}
\]
function y = nest( d, c, x, b )
if nargin < 4, b = zeros(d, 1); end
y = c(d + 1);
for i = d : -1 : 1
y = y.*(x - b(i)) + c(i);
end
end
等比数列的实现方式：
\[P(x) = \frac{1 - (-x)^{100} } {1 - (-x)}
\]
function y = nestup(x, n, a)
if nargin < 3, a = 1; end
q = -1 * x;
y = (a * (1 - q ^ n)) / (1 - q);
end
高精度计算的处理
\[\sqrt{c^2 + d} - c
\]
转换为下述形式
\[\frac{c^2}{\sqrt{c^2 + d} + c}
\]
c = 246886422468;
d = 13579;
x = sqrt(c * c + d) - c; % x = 0 wrong answer
% x must equals to y
y = d / (sqrt(c * c + d) + c) % y = 2.7500e-08
二分法的实现：
function xc = CalDetBisect(f, a, b, tol)
fa = f(a);
fb = f(b);
if sign(fa) * sign(fb) >= 0
error(\'f(a)f(b)<0 not satisified!\')
end
while (b - a) / 2 > tol
c = (a + b) / 2;
fc = f(c);
if fc == 0
break;
end
if sign(fc) * sign(fa) < 0
b = c;
fb = fc;
else
a = c;
fa = fc;
end
end
xc = (a + b) / 2;
end
