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From: Steve on 30 Apr 2010 13:47
Hi guys,
I'm just curious if anyone disagrees with the following conclusions that I've drawn.
If one considers two functions

Q1(X,Y)=0.5*(A*(2*X*Y)-2*(C*Y+D*X)+E)
Q2(X,Y)=0.5*(A*(Y^2-X^2)-2*(D*Y-C*X)+F)

with function values Q1(X,Y), Q2(X,Y) where the point X=Y=0 is excluded, and all coefficients A,C,D,E,F are considered to be non-zero, the claim is that the function values Q1(X,Y), Q2(X,Y) have to be known for at least three different points P(X,Y) to determine all unknowns A,C,D,E,F.

Does anyone disagree?

Thanks,
Steve
From: Bruno Luong on 30 Apr 2010 16:02
"Steve " <guch.steve408(a)gmail.com> wrote in message <hrf52o$lp2$1(a)fred.mathworks.com>...
> Hi guys,
> I'm just curious if anyone disagrees with the following conclusions that I've drawn.
> If one considers two functions
>
> Q1(X,Y)=0.5*(A*(2*X*Y)-2*(C*Y+D*X)+E)
> Q2(X,Y)=0.5*(A*(Y^2-X^2)-2*(D*Y-C*X)+F)
>
> with function values Q1(X,Y), Q2(X,Y) where the point X=Y=0 is excluded, and all coefficients A,C,D,E,F are considered to be non-zero, the claim is that the function values Q1(X,Y), Q2(X,Y) have to be known for at least three different points P(X,Y) to determine all unknowns A,C,D,E,F.
>
> Does anyone disagree?

I will add that it is possible to build a case where 3 distinct points are not enough to determine A-F. This is however not contradict with your claim.

Bruno
From: Steve on 30 Apr 2010 18:16
Hi Bruno,
Which distinct points would cause three points not to be sufficient?
In the case that you are referring to, are any of the coefficients zero?

Thanks,
Steve



"Bruno Luong" <b.luong(a)fogale.findmycountry> wrote in message <hrfd0e$60r$1(a)fred.mathworks.com>...
> "Steve " <guch.steve408(a)gmail.com> wrote in message <hrf52o$lp2$1(a)fred.mathworks.com>...
> > Hi guys,
> > I'm just curious if anyone disagrees with the following conclusions that I've drawn.
> > If one considers two functions
> >
> > Q1(X,Y)=0.5*(A*(2*X*Y)-2*(C*Y+D*X)+E)
> > Q2(X,Y)=0.5*(A*(Y^2-X^2)-2*(D*Y-C*X)+F)
> >
> > with function values Q1(X,Y), Q2(X,Y) where the point X=Y=0 is excluded, and all coefficients A,C,D,E,F are considered to be non-zero, the claim is that the function values Q1(X,Y), Q2(X,Y) have to be known for at least three different points P(X,Y) to determine all unknowns A,C,D,E,F.
> >
> > Does anyone disagree?
>
> I will add that it is possible to build a case where 3 distinct points are not enough to determine A-F. This is however not contradict with your claim.
>
> Bruno
From: Bruno Luong on 1 May 2010 02:33
"Steve " <guch.steve408(a)gmail.com> wrote in message <hrfkr4$8ie$1(a)fred.mathworks.com>...
> Hi Bruno,
> Which distinct points would cause three points not to be sufficient?
> In the case that you are referring to, are any of the coefficients zero?
>
> Thanks,

Steve,

Oops, I think I made a mistake when I wrote it. I just check the example, and it no longer works.

Bruno
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