i have this problem:
z= a*(x^c) + b *(y^d),
where x,y,z are the variables , a,c ,c,d constants.
i have 4 set of values for z, x, and y available i.e
z1=a*(x1^c) + b *(y1^d) ---1
z2=a*(x2^c) + b *(y2^d) ----- 2
z1=a*(x3^c) + b *(y3^d)----- 3
z1=a*(x4^c) + b *(y4^d) ------4
how do i solvethese to know a,b,c,d.
if i use polynomial fit, in matlab, it wld do for 2 variables, say z vs x , z vs y, and if i add those
2 equations, with coefficients divided by two, same thing when done for some other x,y,z gives diffrent coefficients.
similarly, if i solve 1 and 2 assuming c=1,d=1, c=2,d=2, etc, i get a,b which i get diffenet for =n 3 and 4, which shd be same.
so, anyone, with ideas? is there matrix method?or approximation method?