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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.

    Thanks,
    Luca
     
  2. jcsd
  3. Jan 27, 2014 #2

    Stephen Tashi

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    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.
     
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