Re: Curve fitting

If you use any linear Least Squares (LS) algorithm, you can
practically force a constraint by increasing the weight of the
respective point to near infinity. In this context, a point (xi, yi)
refers to the ith rows in X and y of the problem

min ||y - Xa||
a

You replace (xi, yi) with (w*xi, w*yi). In the limit w->oo, the
constraint is exact, i.e., (yi - xiTa) -> 0, but you can practically
use a large finite value w, so that (yi - xiTa) is very small. The
allowable size of the weight will depend on the specific algorithm
because typical algorithms will be unstable for sufficiently large
weights and you will have to determine the largest weight before this
happens. However, row sequential LS via the Sherman-Morrison formula
is stable with infinite weights because the weight w conveniently
appears as a reciprocal 1/w = 0. If you constrain only one point, the
exact row sequential update can be conveniently done on a solution
previously found by QR or Cholesky decomposition. If you are
interested, I can look up the exact procedure for you.


On Nov 16, 2:05 pm, eoz1...@xxxxxxxxxxxxxx wrote:
Hi everyone,

I have a question regarding curve fitting to data.
My question is:
If I have some data points one of them is (0,0) and when I fit them to
a curve, how can I control this fitting curve and force it to pass a
definite point like (0,0).

Could anyone give help in this question?

Thank you in advance.

RainyCloud

.

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