Curve fitting using custom model

Given set of x and y, how can I solve the parameter a, b and c in the model

y = a * x^b + c

to best fit the given data?

As I will further implement the algorithm in C++, I would prefer not using built-in Matlab functions to solve parameters.

Could anyone please suggest an algorithm? Many thanks, Kyle.

[Walter Roberson]

Are a and x certain to be non-negative ?

[Kyle Wang]

the given data set x_given and y_given are vectors of positive double numbers. a, b and c could be negative or positive.

Answer 1

[Walter Roberson]

G = @(abc) sum((abc(1)*x0.^abc(2)+abc(3)-y0).^2);
ABC = fminsearch(G, [rand,rand,rand], 'MaxIters', 10000)

the result will not necessarily be exactly correct, and you can pass ABC back in instead of [rand,rand,rand], but I did find that with my test sometimes it cycled near the answer.

fminsearch is a gradient descent method.

Answer 2

[Torsten]

Chapter 15.5 of

http://www2.units.it/ipl/students_area/imm2/files/Numerical_Recipes.pdf

Best wishes

Torsten.

[Elias]

sounds interesting thanks