Discrete equation with two unknown variables
2 views (last 30 days)
Show older comments
[EDIT: 20110523 16:16 CDT - clarify - WDR]
Hi,
I am looking for a simple way to find out the solution for this equation:
y1 = a*x1/(1+b)*x1
y2 = a*x2/(1/b)*x2
a and b are unkown but x1, x2, y1, y2 are known. I need discrete solutions for this equation and not 1 and 0 as solution. How can I compute this in MatLab, I know it is rather simple by head, but I have been cracking my head over this for several days and never am sure of what I find is right.
Accepted Answer
Arnaud Miege
on 20 May 2011
This can be rewritten as:
a*x1^2 - b*y1 = y1
a*x2^2 - b*y2 = y2
or in matrix form:
A * [a b]' = [y1 y2]'
where:
A = [x1^2 -y1; x2^2 -y2];
So:
x1 = 2;
x2 = 3.3;
y1 = 9;
y2 = 2.9;
A = [x1^2 -y1; x2^2 -y2];
RHS = [y1 y1]';
solution = A\RHS;
a = solution(1);
b = solution(2);
HTH,
Arnaud
12 Comments
Arnaud Miege
on 23 May 2011
Your A and RHS are wrong:
A = [x1^2 -y1; x2^2 -y2];
RHS = [y1 y2]';
solution = A\RHS;
a = solution(1)
b = solution(2)
This gives a = 0 and b = 1:
>> a*x1^2 - b*y1
ans =
37601
>> y1
y1 =
37601
>> a*x2^2 - b*y2
ans =
102743
>> y2
y2 =
102743
>> det(A)
ans =
2.1767e+014
More Answers (2)
Oleg Komarov
on 20 May 2011
x1 = 2;
x2 = 3.3;
y1 = 9;
y2 = 2.9;
f = @(ab) [ab(1)*x1/(1+ab(2))*x1 - y1
ab(1)*x2/(1/ab(2))*x2 - y2];
R = fsolve(f,[0 0]);
4 Comments
Arnaud Miege
on 20 May 2011
fsolve is part of the Optimization Toolbox, see http://www.mathworks.com/help/releases/R2011a/toolbox/optim/ug/fsolve.html
Andrei Bobrov
on 20 May 2011
f1 = @(x,x1,x2,y1,y2)[y1-x(1)*x1.^2./(1+x(2));y2-x(1)*x2.^2/(1./x(2))];
x1 = 1;x2 = 2;y1=10;y2=15;
fsolve(@(x)f1(x,x1,x2,y1,y2),[10,10]);
0 Comments
See Also
Categories
Find more on Systems of Nonlinear Equations in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!