>> x=[1450 1460 1470 1480 1490 1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600]
x =
Columns 1 through 7
1450 1460 1470 1480 1490 1500 1510
Columns 8 through 14
1520 1530 1540 1550 1560 1570 1580
Columns 15 through 16
1590 1600
>> y=[0.1 0.2 0.364 0.584 0.844 1.096 1.38 1.72 1.979 2.293 2.624 2.96 3.304 3.67 4.13 4.484]
y =
Columns 1 through 9
0.1000 0.2000 0.3640 0.5840 0.8440 1.0960 1.3800 1.7200 1.9790
Columns 10 through 16
2.2930 2.6240 2.9600 3.3040 3.6700 4.1300 4.4840
>> syms A B C
>> y1=A+B*x.^2+C*x.^(-2)
y1 =
[ A + 2102500*B + (4492144097854597*C)/9444732965739290427392, A + 2131600*B + (4430818617817269*C)/9444732965739290427392, A + 2160900*B + (4370740416372479*C)/9444732965739290427392, A + 2190400*B + (8623751794867869*C)/18889465931478580854784, A + 2220100*B + (8508385177009405*C)/18889465931478580854784, A + 2250000*B + (4197659095884129*C)/9444732965739290427392, A + 2280100*B + (8284490123888681*C)/18889465931478580854784, A + 2310400*B + (8175842248735535*C)/18889465931478580854784, A + 2340900*B + (1008664719310873*C)/2361183241434822606848, A + 2371600*B + (995607708481541*C)/2361183241434822606848, A + 2402500*B + (1965605195783411*C)/4722366482869645213696, A + 2433600*B + (3880971797230149*C)/9444732965739290427392, A + 2464900*B + (3831690115517583*C)/9444732965739290427392, A + 2496400*B + (7566682395240579*C)/18889465931478580854784, A + 2528100*B + (933975412932567*C)/2361183241434822606848, A + 2560000*B + (7378697629483821*C)/18889465931478580854784]
>> for i=1:length(x)
e(i,1)=y1(i)-y(i);
T=coeffs(e(i,1));
R(i,:)=T(end:-1:1);
end
>> e
e =
A + 2102500*B + (4492144097854597*C)/9444732965739290427392 - 1/10
A + 2131600*B + (4430818617817269*C)/9444732965739290427392 - 1/5
A + 2160900*B + (4370740416372479*C)/9444732965739290427392 - 91/250
A + 2190400*B + (8623751794867869*C)/18889465931478580854784 - 73/125
A + 2220100*B + (8508385177009405*C)/18889465931478580854784 - 211/250
A + 2250000*B + (4197659095884129*C)/9444732965739290427392 - 137/125
A + 2280100*B + (8284490123888681*C)/18889465931478580854784 - 69/50
A + 2310400*B + (8175842248735535*C)/18889465931478580854784 - 43/25
A + 2340900*B + (1008664719310873*C)/2361183241434822606848 - 1979/1000
A + 2371600*B + (995607708481541*C)/2361183241434822606848 - 2293/1000
A + 2402500*B + (1965605195783411*C)/4722366482869645213696 - 328/125
A + 2433600*B + (3880971797230149*C)/9444732965739290427392 - 74/25
A + 2464900*B + (3831690115517583*C)/9444732965739290427392 - 413/125
A + 2496400*B + (7566682395240579*C)/18889465931478580854784 - 367/100
A + 2528100*B + (933975412932567*C)/2361183241434822606848 - 413/100
A + 2560000*B + (7378697629483821*C)/18889465931478580854784 - 1121/250
>> MC=double(R(1:end, 1:end-1))
MC =
1.0e+006 *
0.0000 2.1025 0.0000
0.0000 2.1316 0.0000
0.0000 2.1609 0.0000
0.0000 2.1904 0.0000
0.0000 2.2201 0.0000
0.0000 2.2500 0.0000
0.0000 2.2801 0.0000
0.0000 2.3104 0.0000
0.0000 2.3409 0.0000
0.0000 2.3716 0.0000
0.0000 2.4025 0.0000
0.0000 2.4336 0.0000
0.0000 2.4649 0.0000
0.0000 2.4964 0.0000
0.0000 2.5281 0.0000
0.0000 2.5600 0.0000
>> I=double(R(:,end))
I =
-0.1000
-0.2000
-0.3640
-0.5840
-0.8440
-1.0960
-1.3800
-1.7200
-1.9790
-2.2930
-2.6240
-2.9600
-3.3040
-3.6700
-4.1300
-4.4840
>> S=linsolve(MC,I)
Warning: Rank deficient, rank = 2, tol = 3.3140e-008.
S =
20.8467
-0.0000
0
>> A=S(1)
A =
20.8467
>> B=S(2)
B =
-9.8078e-006
>> C=S(3)
C =
0