Solving matrix of equations

Hi

Can someone help me with following problem: I got this matrix with 5 equations where a1,a2,a3,a4,a5 and b1,b2,b3,b4,b5 are known numbers (for example a1=1,a2=1.5,a3=1.3,a4=1.7,a5=0.8 and b1=2,b2=4,b3=3,b4=5,b5=2.5)

 a1=C1*(b1 )^(C2 )

 a2=C1*(b2 )^(C2 )

 a3=C1*(b3 )^(C2 )

 a4=C1*(b4 )^(C2 )

 a5=C1*(b5 )^(C2 )

I need to find the best fitting numbers for C1 and C2. Is there some function in matlab I can use?

thanks in advance!

Answer 1

[Andrei Bobrov]

use function nlinfit from Statistics Toolbox

a =[1          1.5          1.3          1.7          0.8]
b =[2            4            3            5          2.5]

fout = @(c,x)c(1)*x.^c(2)
c2 = nlinfit(b,a,fout,[1 1])
fout(c2,b)

ans =
      0.88459       1.4641       1.1878        1.722       1.0404

[b1,i1] = sort(b);
a1 = a(i1);
x = linspace(b1(1),b1(end),20);
plot(b1,a1,'ro',x,fout(c2,x));grid on

[Stijn]

Is it correct that I find C1 and C2 in c2?!?

in this example [0.5344,0.7269]

thanks!

[Andrei Bobrov]

yes

[Stijn]

Thanks again! :D

Answer 2

[Aldin]

I can solve your problem. Numerical mathematic If you are familiar with approximation newton's method you can solve it. See this: <http://www.google.com/imgres?q=Numerical+mathematical+approximations&um=1&hl=en&sa=N&biw=1280&bih=709&tbm=isch&tbnid=5WBPaYfADVwhlM:&imgrefurl=http://dmpeli.mcmaster.ca/Matlab/Math1J03/LectureNotes/Lecture3_2.htm&docid=sr12MXThpioXRM&imgurl=http://dmpeli.mcmaster.ca/Matlab/Math1J03/LectureNotes/Lecture3_2_files/image004.jpg&w=456&h=342&ei=ojrqTo66DcKL4gTo2pzoCA&zoom=1&iact=hc&vpx=870&vpy=353&dur=814&hovh=157&hovw=208&tx=102&ty=74&sig=102940788651406343855&page=6&tbnh=157&tbnw=208&start=93&ndsp=17&ved=1t:429,r:9,s:93>

[Stijn]

Can you try it for me?

thanks in advance!