Basic question about numerical hessian

[pamparana]

Hello all,

Suppose I have a simple 1-D signal and I want to compute the hessian. In that case, it should generalise for second derivative for normal scalar functions.



So, I observe the signal as $v = [x_1, x_2, x_3, x_4...]$. Then, numerically the hessian is given as (assuming I am only conputing it at interior points):

$h = [0, (x_1+x_3 -2x_2), (x_2+x_4-2x_3), 0]$.

Now, according to the document for example here (http://planetmath.org/HessianMatrix), I should be able to write this as:

$h = v * H * v'$. Where H is some transformation. I am trying to figure out what this H should be for my simple 1-D case without any luck.

I would greatly appreciate any help anyone can give me with computing this Hessian operator.

Thanks,
Luca

 

[Stephen Tashi]

Now, according to the document for example here (http://planetmath.org/HessianMatrix), I should be able to write this as:

$h = v * H * v'$. Where H is some transformation.

The page at PlanetMath says $v H v^T$ is a quadratic form, so it is a scalar valued function. The thing you are calling $h$ looks like a vector.