- #1
kingwinner
- 1,270
- 0
Homework Statement
Consider the function f(a)=
1
∫ [g(x)-(anxn+an-1xn-1+...+a0)]2 dx
0
where a=(a0,a1,...an) and g is some known function defined on [0,1].
From this, we can show that
Thus, the Hessian of f at a = [2/(j+k+1)] j=0,1,2,...n; k=0,1,2,...,n.
Fact: This Hessian matrix is positive definite.
Now how can we prove that this (n+1) x (n+1) matrix is positive definite? (i.e. vT (Hessian) v >0 for all v E Rn+1, v≠0.)
When I multiply out the vT (Hessian) v, it just doesn't seem clear to me at all that it is >0.
Homework Equations
N/A
The Attempt at a Solution
Shown above.
Any help is appreciated!