Using Newton Raphson for Root Finding and Parameters' Estimation in Matlab -

i have cubic root equation. wrote matlab code using newton-raphson find roots. want parameter estimation (tuning of cubic root equation parameters able give better prediction) using experiment data. can me on how this?

thanks anticipated regards, isa

if understand correctly, should using roots find roots of cubic polynomials, this: roots([4 -2 3 -1]) 4x^3 - 2x^2 +3x -1.

you can calculate how root changes respect each coordinate. in p(x)=0, 1 finds dp/da + p'(x)*dx/da = 0 parameter a. if a_3 coefficient of x^3, 1 gets dx/d(a_3) = -(x^3)/p'(x). can use gradient of root respect coefficients, , conduct gradient descent or better method move roots toward targets.