我變分法是很多年前學的，而且只懂皮毛......
底下這個問題不好意思我用英文輸入啦 :P
有請版友指點，多謝～～
Consider real valued functions in the closed domain [0, 1]
Find f(x) that minimizes: Integrate{ g(x)^2 / f(x) },
with respect to a given g(x), integrate over x from 0 to 1,
subject to the constraints
(1) f > 0 for all x in [0, 1]
(2) |f| = 1, that is, Integrate{ f(x) } over x = 0 to 1 is unity.
Suppose everything you need to know about g(x) is completely specified.
(the derivative or anti-derivative of g(x) etc)
In general g(x) can be just some real valued integrable function (that doesn't
even have to be piece-wise continuous), but if needed we can focus on the solution
f(x) for some smooth g(x).
p.s.
Some of you might notice that f is a probability density.
In fact, this question is simplified from a question regarding minimizing
the variance of some stuff.
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