Solve y = f(y,x)

robot

Hi,

I would like to use JMP to solve for y in an equation of the form y = f(y,x).  A more precise equation is attached.  This problem seem similar to that discussed in Numerical solver add-in, although a clear solution is not mentioned.

In the attached equation, y is response, x is predictor, and a - k are fitting parameters.

What is the best way for JMP to tackle this?  I am using JMP11.  Thanks!

2015_04_30 Formula.jpg

Hegedus

Hi,

I will make an assumptions: You have a series of data points with both x and y measured.

The way I have handled this in the past since you have an implicit equation, is to recast it as an explicit equation by creating a new function.

If you subtract the left hand elements from both sides you get an equation equal to zero. 

0 = right hand(x,y) -  left hand(x,y)

Now substitute a variable for zero so you have a new equation.

z = right hand(x,y) - left hand(x,y)

Now set Z at all points equal to 0 (zero) and solve as a multi-variable problem.

Caveat I have not done a rigorous error analysis on this technique, but just used in the past with success.

Good Luck.

Andy