fit to multivariate Taylor series expansion using java

Question

I am trying to find the Java library which can fit data to multivariate Taylor series expansion.

Here is the mathematical description of the problem:

I have a dependent variable y and several independent variables, xi (e.g., x1, x2, x3). The Taylor expansion of y around each xi can be written as:

y = a0 + a1*x1 + a2*x2 + a3*x3

+ a11 * x1 * x1 + a22 *x2 * x2 + a33 *x3 *x3

+ a12 * x1 * x2 + a13 * x1 * x3 + a23 * x2 * x3 

I have many observations of y and the corresponding x1, x2, x3.

[y, x1, x2, x3]_1

[y, x1, x2, x3]_2

[y, x1, x2, x3]_3

.....

[y, x1, x2, x3]_n

( _n stands for an observation )

I would like to fit these observations to the above Taylor expansion and find out the values of the parameters (a0, a1, a2, a3, a11 etc).

I am trying to find a java math library to do the job.
It looks that Apache Commons Math may do the job.
But I really could not find which class should be used.

Any suggestions/help is highly appreciated.

Thanks,