MATLAB: What is properly method to optimization of four parameter to be one value

mathematicsoptimizationpolynomial equation

Hello all. I have 4 parameters for 4 equations that I just want to optimize those parameter to one value to be used for these 4 equation. Is there method for this task? ex. Y1=aX1; Y2=bX2; Y3=cX3; Y4=dX4 and want to optimize these a,b,c,d to be A for this equation.

Best Answer

So you have four data points (X1,Y1), (X2,Y2), (X3,Y3), (X4,Y4) and you want to find the "best" A such that

[Y1 Y2 Y3 Y4] = A*[X1 X2 X3 X4]

If this is the case,

A = (X1*Y1+X2*Y2+X3*Y3+X4*Y4)/(X1^2+X2^2+X3^2+X4^2)

Best wishes

Torsten.

Related Solutions

MATLAB: How to fit a curve to 3 points automatically

Maybe something like

A=[x1^2 x1 1
   x2^2 x2 1
   x3^2 x3 1];
rhs=[y1 ; y2 ; y3];
sol=A\b;
func=@(x)sol(1)*x.^2+sol(2)*x+sol(3);
x=x1:0.1:x2;
y=func(x);
plot(x,y)

where (x1,y1), (x2,y2), (x3,y3) are the points in question ?

Best wishes

Torsten.

MATLAB: Using fsolve over a range of equations.

Solve the equations once and then plug in the values.

for z = 100:105
  x1=velprof(z,y1);
  x2=velprof(z,y2);
  x3=velprof(z,y3);
  x4=velprof(z,y4);
  c = [ (((x3*y4-x4*y3)*x2^2+(-x3^2*y4+x4^2*y3)*x2+x3*x4*y2*(-x4+x3))*x1^3+((-x3*y4+x4*y3)*x2^3+(-x4^3*y3+x3^3*y4)*x2+y2*x3*x4^3-x3^3*x4*y2)*x1^2+((x3^2*y4-x4^2*y3)*x2^3+(x4^3*y3-x3^3*y4)*x2^2+x3^2*x4^2*y2*(-x4+x3))*x1-x3*x2*x4*y1*(-x4+x3)*(x2-x4)*(x2-x3))/((-x4+x3)*(x2-x4)*(x2-x3)*(x1-x4)*(x1-x3)*(x1-x2)), ...
  (((-y2+y1)*x4^2+(y2-y4)*x1^2-x2^2*(y1-y4))*x3^3+((-y1+y2)*x4^3+(y4-y2)*x1^3+x2^3*(y1-y4))*x3^2+((y3-y2)*x1^2+x2^2*(y1-y3))*x4^3+((y2-y3)*x1^3-x2^3*(y1-y3))*x4^2+x1^2*x2^2*(y3-y4)*(x1-x2))/((-x4+x3)*(x2-x4)*(x2-x3)*(x1-x4)*(x1-x3)*(x1-x2)), ...
  (((y4-y3)*x2+(y2-y4)*x3-x4*(y2-y3))*x1^3+((y3-y4)*x2^3+(y4-y2)*x3^3+x4^3*(y2-y3))*x1+((-y1+y4)*x3+x4*(y1-y3))*x2^3+((y1-y4)*x3^3-x4^3*(y1-y3))*x2-x3*x4*(-x4+x3)*(x3+x4)*(-y2+y1))/((-x4+x3)*(x2-x4)*(x2-x3)*(x1-x4)*(x1-x3)*(x1-x2)), ...
  (((y3-y4)*x2+(y4-y2)*x3+x4*(y2-y3))*x1^2+((y4-y3)*x2^2+(y2-y4)*x3^2-x4^2*(y2-y3))*x1+((y1-y4)*x3-x4*(y1-y3))*x2^2+((-y1+y4)*x3^2+x4^2*(y1-y3))*x2+x3*x4*(-y2+y1)*(-x4+x3))/((-x4+x3)*(x2-x4)*(x2-x3)*(x1-x4)*(x1-x3)*(x1-x2)) ];
  disp(z)
  disp(c)
end

Best Answer

Related Solutions

MATLAB: How to fit a curve to 3 points automatically

MATLAB: Using fsolve over a range of equations.

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