2nd Order Taylor Series Formula inv. the Hessian Matrix, etc. - what is the x vector?

by jaguar7
Tags: formula, hessian, matrix, order, series, taylor, vector
jaguar7 is offline
Nov15-10, 07:09 PM
P: 42
The formula given by my instructor for a Taylor Series approximation of the second order at point (a,b) is f(a,b) + grad(f(a,b))x + 1/2 H(f(a,b)) x

If you recognize this formula, do you know what the x vector is?

Note: x is the x-vector, and H represents the Hessian Matrix. Thanks!

The Hessian Matrix is the matrix with values [fxx, fxy, fyx, and fyy], where fxx represents the second partial derivative. Not sure the proper terminology for it...... df^2 / (dx)^2 (where d is a delta (not d) to represent partial dif.)
Phys.Org News Partner Science news on Phys.org
Cougars' diverse diet helped them survive the Pleistocene mass extinction
Cyber risks can cause disruption on scale of 2008 crisis, study says
Mantis shrimp stronger than airplanes
HallsofIvy is offline
Nov16-10, 09:19 AM
Sci Advisor
PF Gold
P: 38,894
x is the vector <x- a, y- b>. And you need a quadratic in the second term- it should be
[tex]f(a, b)+ \begin{bmatrix}\frac{\partial f}{\partial x}(a, b) & \frac{\partial f}{\partial y}(a, b)\end{bmatrix}\begin{bmatrix}x- a \\ y- b\end{bmatrix}+ \frac{1}{2}\begin{bmatrix}x- a & y- b\end{bmatrix}\begin{bmatrix}\frac{\partial^2 f}{\partial x^2}(a,b) & \frac{\partial^2 f}{\partial x\partial y}(a,b) \\ \frac{\partial^2 f}{\partial x\partial y}(a,b) & \frac{\partial^2 f}{\partial y^2}(a,b)\end{bmatrix}\begin{bmatrix} x- a \\ y- b\end{bmatrix}[/tex]

Register to reply

Related Discussions
function two wariables - hessian matrix is 0 Calculus & Beyond Homework 3
What's Hessian matrix ??? Calculus 2
Hessian matrix Calculus & Beyond Homework 4
Hessian matrix. Calculus & Beyond Homework 3
Hessian Matrix\Max Min Analysis, Eigenvalues... etc Calculus & Beyond Homework 1