Newton-Raphson?

Question

The function

F(x,y)=x^3+y^3-12(x+y)+6xy Has a minimum near (1.1,1.1)

How do I find this minimum? I know how to work out a function with one variable but two is giving problems.

Answer 1

Dude, you need to express this using matrices. To solve using newton raphson you need the values of the variables at a point and their gradient at that value set. In matrix land the gradient (derivative) is called the Jacobian matrix. If you have two variables, the Jacobian is a 2x2 matrix.

Numerical Recipes tells you a lot about this; the text that goes with the code is very helpful with the maths and is available online (somewhere) for free.

Answer 2

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