Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Basic question about numerical hessian

  1. Jan 27, 2014 #1
    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 [itex]v = [x_1, x_2, x_3, x_4...][/itex]. Then, numerically the hessian is given as (assuming I am only conputing it at interior points):

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

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

    [itex]h = v * H * v'[/itex]. 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.

  2. jcsd
  3. Jan 27, 2014 #2

    Stephen Tashi

    User Avatar
    Science Advisor

    The page at PlanetMath says [itex] v H v^T [/itex] is a quadratic form, so it is a scalar valued function. The thing you are calling [itex] h [/itex] looks like a vector.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook