Re: Need help with method of least squares
- From: pereges <Broli00@xxxxxxxxx>
- Date: Mon, 4 Aug 2008 23:59:33 -0700 (PDT)
Ok this is what my problem is. If you expand those 3 matrix equations
you get six equations in total :
Let (del n / del u) dot u = A.
(del n / del v) dot u = B.
(del n / del u) dot v = C.
(del n / del v) dot v = D.
That means you have four variables and 6 equations.
A * (e0 dot u) + B * (e0 dot v) = (n2 - n1) dot u ----- (1)
C * (e0 dot u) + D * (e0 dot v) = (n2 - n1) dot v ----- (2)
A * (e1 dot u) + B * (e1 dot v) = (n0 - n2) dot u ------ (3)
C * (e1 dot u) + D * (e1 dot v) = (n0 - n2) dot v ------ (4)
A * (e2 dot u) + B * (e2 dot v) = (n0 - n2) dot u ------ (5)
C * (e2 dot u) + D * (e2 dot v = (n0 - n2) dot v ------- (6)
Now if you want to use least squares method, we can write an
expression :
(RHS1 - LHS1)^ 2 + (RHS2 - LHS2) ^ 2 + (RHS3 - LHS3) ^2 + (RHS4 -
LHS4) ^2 + (RHS5 - LHS5) ^ 2 + (RHS6- LHS6) ^2
Now to find A, B , C , D ..you would want to find the partial
derivative of above expression with respect to A , B , C and D and
then equate them to zero. Then you get 4 linear equations and solve
them to find the values of A, B, C, D. Is this correct ?
.
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