       Re: Hessian Matrix of a Numerical Defined Function

• To: mathgroup at smc.vnet.net
• Subject: [mg106615] Re: Hessian Matrix of a Numerical Defined Function
• From: dh <dh at metrohm.com>
• Date: Mon, 18 Jan 2010 05:39:39 -0500 (EST)
• References: <his71a\$la0\$1@smc.vnet.net>

```
Hi,

as long as the derivatives are continuous there should be no difference

between fxy and fyx. Therefore, it is not clear why ND should not give

the correct result for the mixed derivative. Maybe your function does

not behave properly? Can you give a simple example?

Daniel

Anh Ngoc LAI wrote:

> Dear all,

>

> I have to calculate the numerical hessian matrix of a numerical defined function. So i use two time ND, but the result seems to me that is not correct.

>

> Let take the function as  f(x,y), and the hessian matrix at point (1,1) will be:

>

> (1) ND[f[x,1],{x,2},1]

>

> (2) ND[f[1,y],{y,2},1]

>

> and

>

> (3) ND[ND[f[x,y],{x,1},1],{y,1},1]

>

> But it seems that the result given by (3) is not right, so that i can not go further.

>

> Any suggestion will be very helpful.

>

> Thanks.

>

> LAI.

>

```

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