$x^{2}+y^{2}-8 x+16 y-1=0$ is the equation of a circle with center $(h, k)$ and radius $r$ for: \[ h= \]

Step 1 ：The general equation of a circle is given by \((x-h)^2 + (y-k)^2 = r^2\). Comparing this with the given equation, we can see that the coefficients of \(x\) and \(y\) are \(-2h\) and \(2k\) respectively.

Step 2 ：Therefore, we can find \(h\) by dividing the coefficient of \(x\) by \(-2\).

Step 3 ：So, \(h = 4.0\)

Step 4 ：Final Answer: \(\boxed{4.0}\)