How can I find the coefficients of a polynomial equation for fit the curve in MATLAB?

hello. my polynomial equation is ( V)=c0+c1*T+c2*(t^2)-c3*P-c4*P*T i want use data for find c0 ,c1, ...c4 coefficients (i want fit data with this equation)

my p,v,t data is

100000 , 0.956 , 19.4

100000 , 0.9717 , 71.1

10000000 , 0.959 , 41.8

80000000, 0.9725 , 161 ...

thank you.

[Image Analyst]

Hosein, can you move this down to the Answers section below, rather than up here in Comments, which is used to ask people for clarification of their question. You can even earn credit if it's down there.

[hosein Javan]

my mistake. my appologies.

Answer 1

[hosein Javan]

if "p" and "t" are both independant variables then your problem is in the form of "y=f(x,z)" or "v=f(p,t)".

x=[
    19.4
    71.1
    41.8
    161
    180
];  % t
y=[ 
    100000
    100000
    10000000
    80000000
    100000000
];  % p
z=[
    0.956
    0.9717
    0.959
    0.9725
    0.9999
];  % z
sf = fit([y, x],z,'poly21')
plot(sf,[y,x],z)

look at command window,

sf(x,y) = p00 + p10*x + p01*y + p20*x^2 + p11*x*y

V(t,p) = c0 +c1*T - c3*P +c2*(t^2) - c4*T*P

by comparing you will understant that:

c0=p00

c1=p10

c3=-p01

c2=p20

c4=-p11;