Discrete equation with two unknown variables

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Ruben Verkempynck
Ruben Verkempynck 2011-5-20
[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.
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Ruben Verkempynck
Ruben Verkempynck 2011-5-20
Guys,
I made a huge mistake the equation should be:
y1 = a*x1/(1+b)*x1
y2 = a*x2/(1+b)*x2

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采纳的回答

Arnaud Miege
Arnaud Miege 2011-5-20
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
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Arnaud Miege
Arnaud Miege 2011-5-23
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

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更多回答（2 个）

Oleg Komarov
Oleg Komarov 2011-5-20
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]);
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Arnaud Miege
Arnaud Miege 2011-5-20
fsolve is part of the Optimization Toolbox, see http://www.mathworks.com/help/releases/R2011a/toolbox/optim/ug/fsolve.html

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Andrei Bobrov
Andrei Bobrov 2011-5-20
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]);

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