CODEWITHSUNDEEP
matlabinterpolationnumerical-methodsnewtons-method
bullbo
bullbo

Reputation: 131

Nonlinear interpolation using Newtons method

Given a set of datapoints I'm trying to approximate the coefficients a,b in the function U(x)=8-ax^b using Newtons method in MATLAB.

x = [150 200 300 500 1000 2000]';
y = [2 3 4 5 6 7]';
a=170; b=-0.7; iter = 0; 
for iter=1:5
    f=8-a*x.^(b) -y;
    J = [-x.^b -a*b*x.^(b-1)]; %Jacobis matrix
    h=J\f;
    a=a-h(1); b=b-h(2);
    disp(norm(f))
    iter = iter+1;
end

The results are incorrect and I've not been sucessful of finding the misstep. All help is appreciated.

Upvotes: 1

Views: 349

Answers (2)

user1196549
user1196549

Reputation:

Note that you can easily linearize your model with

Log(8 - U(x)) = Log(a) + b Log(x)

Upvotes: 0

Aziz
Aziz

Reputation: 20735

The jacobi matrix is wrong. Using Newton's method, you're trying to find the values of a and bthat would solve the equations 8-ax^b - y = 0. So, your Jacobi should be the derivatives of f with respect to a and b. That is J = [df/da df/db], resulting in:

J = [-x.^b -a.*x.^b.*log(x)]

and you will get the following curve for the 5 iterations:

Upvotes: 2

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