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2023 Dec 04
1
Fit NLE - was: computer algebra in R
...ld back-substitute hd into the polynomial:
hd = (y - I0 - ID*d0) / (IHD - ID);
f(x, hd, kd) becomes then f(x, y, kd, I0, ID, IHD) = 0;
- f is order 3 in y;
You could fit:
(y^3) ~ f(x, y, kd, I0, ID, IHD) - y^3,
where you subtract the y^3 term from the function f, and add the (y^3) values as a new columng to the data.frame:
data.frame(y3 = y^3, y=y, x=x)
If the values of y are versy small (abs(y) << 1), then it may be wiser to fit:
y ~ f(x, y^2, y^3, kd, I0, ID, IHD) - (y-term);
But I am not an expert in these problems. Other R-users may be more helpful.
2.) Approach 2: Math
I feel that the...