determine the coefficients of a polynomial

How to determine the constant coefficients (A, B, C, D, E) of a polynomial of the form:

y = Ax^0.5 + Bx + Cx^2 + Dx^3 + Ex^4

I already have a vector for x and y.

Answer 1

[John D'Errico]

This is not in fact a true polynomial, although some like to extend that family of functions to allow non-integer exponents.

However, my polyfitn can handle the problem easily. Download it from the file exchange.

Or you can use any of a variety of tools in MATLAB, like regress, lsqr, even backslash.

[VENKATESAN SEETHARAMAN]

I tried using polyfit but I don't think the coefficients generated were right. Is there a possibility that the presence of x^0.5 in the equation makes polyfit work differently?

[John D'Errico]

I told you that your problem is NOT a polynomial. polyfit CANNOT solve the problem. This is not a possibility, but a simple fact.

I also DID tell you that my own polyfitn DOES solve that problem.

[Image Analyst]

Venkatesan, where did you come up with that model anyway? Is there any physical theory/justification for using a model that's the sum of x^0.5 and a regular polynomial? What physical process are you modeling?